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• PhD in Mathematical Finance

The PhD in Mathematical Finance is for students seeking careers in research and academia. Doctoral candidates will have a strong affinity for quantitative reasoning and the ability to connect advanced mathematical theories with real-world phenomena. They will have an interest in the creation of complex models and financial instruments as well as a passion for in-depth analysis.

Learning Outcomes

The PhD curriculum has the following learning goals. Students will:

• Demonstrate advanced knowledge of literature, theory, and methods in their field.
• Be prepared to teach at the undergraduate, master’s, and/or doctoral level in a business school or mathematics department.
• Produce original research of quality appropriate for publication in scholarly journals.

After matriculation into the PhD program, a candidate for the degree must register for and satisfactorily complete a minimum of 16 graduate-level courses at Boston University. More courses may be needed, depending on departmental requirements.

PhD in Mathematical Finance Curriculum

The curriculum for the PhD in Mathematical Finance is tailored to each incoming student, based on their academic background. Students will begin the program with a full course load to build a solid foundation in not only math and finance but also the interplay between them in the financial world. As technology plays an increasingly larger role in financial models, computer programming is also a part of the core coursework.

Once a foundation has been established, students work toward a dissertation. Working closely with a faculty advisor in a mutual area of interest, students will embark on in-depth research. It is also expected that doctoral students will perform teaching assistant duties, which may include lectures to master’s-level classes.

Course Requirements

The minimum course requirement is 16 courses (between 48 and 64 credits, depending on whether the courses are 3 or 4 credits each). Students’ course choices must be approved by the Mathematical Finance Director prior to registration each semester. The following is a typical program of courses.

• GRS EC 701 Microeconomic Theory
• GRS MA 711 Real Analysis
• GRS MA 779 Probability Theory I
• QST FE 918 Doctoral Seminar in Finance
• GRS EC 703 Advanced Microeconomic Theory
• GRS MA 776 Partial Differential Equations
• GRS MA 781 Probability Theory 2
• QST FE 920 Advanced Capital Market Theory
• GRS EC 702 Macroeconomic Theory
• GRS MA 783 Advanced Stochastic Processes
• QST MF 850 Advanced Computational Methods
• QST MF 922 Advanced Mathematical Finance
• GRS EC 704 Advanced Microeconomic Theory
• GRS MA 751 Statistical Machine Learning
• QST MF 810 FinTech Programming
• QST MF 921 Topics in Dynamic Asset Pricing

Additional Requirements

Qualifying examination.

Students must appear for a qualifying examination after completion of all coursework to demonstrate that they have:

• acquired advanced knowledge of literature and theory in their area of specialization;
• acquired advanced knowledge of research techniques; and
• developed adequate ability to craft a research proposal.

Guidelines for the examination are available from the departments. Students who do not pass either the written and/or oral comprehensive examination upon first try will be given a second opportunity to pass the exam. Should the student fail a second time, the student’s case will be reviewed by the Mathematical Finance Program Development Committee (MF PDC), which will determine if the student will be withdrawn from the PhD program. In addition, the PhD fellowship (if applicable) of any student who does not pass either the written and/or oral comprehensive examination after two attempts will be suspended the semester after the exam was attempted.

Dissertation

Following successful completion of the qualifying examination, the student will develop a research proposal for the dissertation. The final phase of the doctoral program is the completion of an approved dissertation. The dissertation must be based on an original investigation that makes a substantive contribution to knowledge and demonstrates capacity for independent, scholarly research.

Doctoral candidates must register as continuing students for DS 999 Dissertation, a 2-credit course, for each subsequent regular semester until all requirements for the degree have been completed. PhD students graduating in September are required to register for Dissertation in Summer Session II preceding graduation.

Academic Standards

Time limit for degree completion.

After matriculation into the PhD program, a candidate for the degree must meet certain milestones within specified time periods (as noted in the table below) and complete all degree requirements within six years of the date of first registration. Those who fail to meet the milestones within the specified time, or who do not complete all requirements within six years, will be reviewed by the PhD PDC and may be dismissed from the program. A Leave of Absence does not extend the six-year time limit for degree completion.

Performance Review

The Mathematical Finance Program Development Committee will review the progress of each doctoral candidate. Students must maintain a 3.30 cumulative grade point average in all courses to remain in good academic standing. Students who are not in good academic standing will be allowed one semester to correct their status. Prior to the start of the semester, the student must submit a letter to the Faculty Director (who will forward it to the PDC) explaining why the student has fallen short of the CGPA requirement and how the student plans to correct the situation. Failure to increase the CGPA to acceptable levels may result in probation or withdrawal from the program, at the discretion of the PhD Program Development Committee (PDC).

Graduation Application

Students must submit a graduation application at least seven months before the date they expect to complete degree requirements. It is the student’s responsibility to initiate the process for graduation. The application is available online and should be submitted through the Specialty Master’s & PhD Center website for graduation in January, May, or August.

If graduation must be postponed beyond the semester for which the application is submitted, students should contact the Specialty Master’s & PhD Center to defer the date. If students wish to postpone their graduation date past the six-year time limit for completion, they must formally petition the PhD Program Development Committee (PDC) for an extension. The petition, which must include the reason(s) for the extension as well as a detailed timetable for completion, is subject to departmental and PDC approval.

PhD degree requirements are complete only when copies of the dissertation have been certified as meeting the standards of Questrom School of Business and have been accepted by Mugar Memorial Library.

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PhD Program in Finance

2023-24 curriculum outline.

The MIT Sloan Finance Group offers a doctoral program specialization in Finance for students interested in research careers in academic finance. The requirements of the program may be loosely divided into five categories: coursework, the Finance Seminar, the general examination, the research paper, and the dissertation. Attendance at the weekly Finance Seminar is mandatory in the second year and beyond and is encouraged in the first year.  During the first two years, students are engaged primarily in coursework, taking both required and elective courses in preparation for their general examination at the end of the second year.  Students are required to complete a research paper by the end of their fifth semester, present it in front of the faculty committee and receive a passing grade.  After that, students are required to find a formal thesis advisor and form a thesis committee by the end of their eighth semester. The Thesis Committee should consist of at least one tenured faculty from the MIT Sloan Finance Group.

Required Courses

The following set of required courses is designed to furnish each student with a sound and well-rounded understanding of the theoretical and empirical foundations of finance, as well as the tools necessary to make original contributions in each of these areas. Finance PhD courses (15.470, 15.471, 15.472, 15.473, 15.474) in which the student does not receive a grade of B or higher must be retaken.

First Year - Summer

Math Camp begins on the second Monday in August. 

First Year - Fall Semester

14.121/14.122 Micro Theory I/II

14.451/14.452 Macro Theory I/II ( strongly recommended)

14.380/14.381 — Statistics/Applied Econometrics

15.470 — Asset Pricing

First Year - Spring Semester

14.123/14.124 Micro Theory III/IV

14.453/14.454 Macro Theory III/IV (strongly recommended)

14.382 – Econometrics

15.471 – Corporate Finance

Second Year - Fall Semester

15.472 — Advanced Asset Pricing

  14.384 — Time-Series Analysis or  14.385 — Nonlinear Econometric Analysis  (Enrolled students receive a one-semester waiver from attending the Finance Seminar due to a scheduling conflict)

15.475 — Current Research in Financial Economics

Second Year - Spring Semester

15.473 — Advanced Corporate Finance

 15.474 — Current Topics in Finance (strongly encouraged to take multiple times)

15.475 — Current Research in Financial Economics

Recommended Elective Courses

Beyond these required courses, students are expected to enroll in elective courses determined by their primary area of interest. There are two informal “tracks” in Financial Economics: Corporate Finance and Asset Pricing. Recommended electives are designed to deepen the student's grasp of material that will be central to the writing of his/her dissertation. Students also have the opportunity to take courses at Harvard University. There is no formal requirement to select one track or another, and students are free to take any of the electives.

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The field of finance covers the economics of claims on resources. Financial economists study the valuation of these claims, the markets in which they are traded, and their use by individuals, corporations, and the society at large.

At Stanford GSB, finance faculty and doctoral students study a wide spectrum of financial topics, including the pricing and valuation of assets, the behavior of financial markets, and the structure and financial decision-making of firms and financial intermediaries.

Investigation of issues arising in these areas is pursued both through the development of theoretical models and through the empirical testing of those models. The PhD Program is designed to give students a good understanding of the methods used in theoretical modeling and empirical testing.

Preparation and Qualifications

All students are required to have, or to obtain during their first year, mathematical skills at the level of one year of calculus and one course each in linear algebra and matrix theory, theory of probability, and statistical inference.

Students are expected to have familiarity with programming and data analysis using tools and software such as MATLAB, Stata, R, Python, or Julia, or to correct any deficiencies before enrolling at Stanford.

The PhD program in finance involves a great deal of very hard work, and there is keen competition for admission. For both these reasons, the faculty is selective in offering admission. Prospective applicants must have an aptitude for quantitative work and be at ease in handling formal models. A strong background in economics and college-level mathematics is desirable.

It is particularly important to realize that a PhD in finance is not a higher-level MBA, but an advanced, academically oriented degree in financial economics, with a reflective and analytical, rather than operational, viewpoint.

Faculty in Finance

Anat r. admati, juliane begenau, jonathan b. berk, greg buchak, antonio coppola, peter m. demarzo, darrell duffie, steven grenadier, benjamin hébert, arvind krishnamurthy, hanno lustig, matteo maggiori, paul pfleiderer, joshua d. rauh, claudia robles-garcia, ilya a. strebulaev, vikrant vig, jeffrey zwiebel, emeriti faculty, robert l. joss, george g.c. parker, myron s. scholes, william f. sharpe, kenneth j. singleton, james c. van horne, recent publications in finance, behavioral responses to state income taxation of high earners: evidence from california, beyond the balance sheet model of banking: implications for bank regulation and monetary policy, fee variation in private equity, recent insights by stanford business, cashless: is digital currency the future of finance, nine stories to get you through tax season, “geoeconomics” explains how countries flex their financial muscles.

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About / Departments

Finance Department | PhD Program

Phd program.

Our faculty, ranked #1 worldwide based on publications in top finance journals (ASU Finance Rankings), consists of more than 30 researchers who study all major areas of finance, making it one of the largest finance faculty in the country. Stern’s finance faculty is highly rated in terms of research output, and faculty members sit on the editorial boards of all major finance journals.

The finance department offers an exceptionally large range of courses devoted exclusively to PhD students. Apart from core PhD courses in asset pricing and corporate finance, students can choose from a range of electives such as household finance, macro-finance, and financial intermediation. PhD students also enjoy the benefits of Stern’s economics department, NYU’s economics department in the Graduate School of Arts and Science (GSAS), and the Courant Institute of Mathematics.

Graduates of Stern’s Finance PhD program have been placed at leading research institutions such as Harvard, MIT, Chicago, Stanford, Wharton, Yale, and UCLA.

Holger Mueller , Finance PhD coordinator

More information on the Finance PhD

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PhD Program

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Wharton’s PhD program in Finance provides students with a solid foundation in the theoretical and empirical tools of modern finance, drawing heavily on the discipline of economics.

The department prepares students for careers in research and teaching at the world’s leading academic institutions, focusing on Asset Pricing and Portfolio Management, Corporate Finance, International Finance, Financial Institutions and Macroeconomics.

Wharton’s Finance faculty, widely recognized as the finest in the world, has been at the forefront of several areas of research. For example, members of the faculty have led modern innovations in theories of portfolio choice and savings behavior, which have significantly impacted the asset pricing techniques used by researchers, practitioners, and policymakers. Another example is the contribution by faculty members to the analysis of financial institutions and markets, which is fundamental to our understanding of the trade-offs between economic systems and their implications for financial fragility and crises.

Faculty research, both empirical and theoretical, includes such areas as:

• Structure of financial markets
• Formation and behavior of financial asset prices
• Banking and monetary systems
• Corporate control and capital structure
• Saving and capital formation
• International financial markets

Candidates with undergraduate training in economics, mathematics, engineering, statistics, and other quantitative disciplines have an ideal background for doctoral studies in this field.

Effective 2023, The Wharton Finance PhD Program is now STEM certified.

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Duke's Fuqua School of Business

The Finance PhD program requires you to complete:

• Course requirements as outlined below
• A second-year research paper
• A finance qualifying exam will be administered and evaluated by the finance faculty committee at the end of Year 2
• Teaching and research assistantship
• A preliminary exam / comprehensive evaluation which will include the presentation of your second-year paper and your performance in the courses and finance qualifier
• Dissertation thesis proposal
• Final dissertation and defense exam

The Finance PhD program provides a sound foundation in the finance and economics disciplines, as well as in related elective courses.

Course Requirements

Complete by end of year 2 the four required finance classes, namely Finance I to Finance IV, and required graduate-level economics classes in the Department of Economics (Microeconomics I, Econometrics I, and Macroeconomics I) and in total, a minimum of 11 graduate-level courses. Specifically:

• Four required finance courses (Finance I to IV)
• Three required economics courses (Microeconomics I, Macroeconomics I, and Econometrics I)
• Electives to meet your specific needs or interests, which can include additional classes in economics (e.g., Microeconomics II, Macroeconomics II, and Econometrics II), mathematics, statistics, decision sciences, and finance

Second-Year Paper

Students are required to form a PhD faculty committee who will guide the student in developing/writing their second-year paper. This paper will be presented in October/November of their third year (roughly at the 2.25-year mark).

Qualifying Exam

At the end of the second year, a finance qualifying exam is offered based on Finance I to Finance IV. This exam is graded and evaluated by the finance faculty committee. The committee can fail a student in any part of the entire exam and determine if the student should take a new qualifier in any subject (or subjects) and/or retake the class that he/she failed in the qualifying exam.

Teaching and Research Assistantship

Students acquire critical classroom experience as professors’ teaching assistants in the courses they offer across programs at Fuqua. Compensated research assistantships beyond that are available on a competitive basis.

Preliminary Exam / Comprehensive Evaluation

The preliminary exam / comprehensive evaluation includes the second-year paper presentation, the performance in the courses and the qualifiers. The finance faculty use these inputs to evaluate the student after the second-year paper presentation. The faculty in conjunction with the student’s PhD faculty committee decides if the student passes the comprehensive exam. In case the student fails the comprehensive exam, he/she may be given a second opportunity as determined by the faculty within 4 months of the first presentation. In case the student fails in their second attempt they will receive a terminal master’s degree in business.

Dissertation Proposal

We suggest students form a dissertation committee in the fall of their fourth year, with the proposal occurring in the spring of the fourth year. Students have until the end of the summer of the fourth year to complete this requirement.

Dissertation Defense

We expect students to defend their dissertation by the end of their fifth year in the program.

Sample Program Schedule

The following is a pro-forma schedule that you might choose, depending on your background, experience, strengths, and interests. At the end of four full semesters (end of Year 2), you should have taken a minimum of 11 graduate-level courses to meet the finance area requirements.

Asterisk indicates key milestone (qualifying, preliminary, and final exams

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DPhil (PhD) studies in Mathematical Finance @ Oxford

The Mathematical and Computational Finance Group (MCFG) at Oxford is one of the largest and most dynamic research environments in mathematical finance in the world.

We combine core mathematical expertise with interdisciplinary approach. We foster lively interactions between researchers coming from different backgrounds and a truly impressive seminar programme, all this within one of the world's top universities, singular through its tradition and unique environment.

If you are passionate about mathematics and research and want to pursue a DPhil in Financial Mathematics, Oxford simply offers one of the best and most exciting places to do it!

 Research Topic and Supervisor Allocation

We welcome students with their own particular ideas of research topic as well as students with a broad interest in the field of Mathematical Finance. You have an opportunity to tell us about your research passions, and indicate potential supervisors, in your application form. This will be followed up during the interview.

In light of this, if you are offered a place, an appropriate supervisor will be proposed prior to your arrival in Oxford. However, there can be some flexibility over this once you arrive.  Keeping with the Oxford tradition, we offer our students independence and respect as early researchers, and always aim to match students with the most appropriate supervisors.

Outstanding students with a strong background in analysis, probability and data science are welcome to apply for our DPhil program. Each year we receive a large number of excellent applications. The selection process is extremely competitive and we can only admit a handful of candidates each year.

In order to apply for DPhil studies in Mathematical & Computational Finance, please indicate your interest in Mathematical and Computational Finance on your application form. Selected applicants will be invited for an interview -- either in person or by video call.

For general information on DPhil please consult our  Doctor of Philosophy (DPhil) admissions pages .

For the CDT Mathematics of Random Systems please consult our  the CDT website .

Or please contact  @email .

Funding for DPhil students is available from a variety of sources. Please note that some funding opportunities have deadlines: it is advised to apply before the deadline in order to maximise your chances of receiving funding.

Funding is also available through the  Centre for Doctoral Training in Mathematics of Random Systems . To apply for this program please How to Apply .

Email:  @email Phone:  +44 (0)1865 615234

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The Finance doctoral program provides students with rigorous training in finance, economics, mathematics and statistics. These tools, plus opportunities for supervised independent research, enable students to make their own contributions to the understanding of financial markets and institutions that lead to productive research careers. The Finance doctoral program trains students to apply empirical methods and theoretical tools to advance our understanding of how financial markets and institutions work, and how they may contribute to economic development. The program aims to produce scholars who develop rigorous and creative research in finance and economics. Students are exposed to a variety of research methods in their coursework, and interact closely with faculty as they develop their own research projects. A distinctive characteristic of our program is its close ties with the Department of Economics, which are fostered by joint seminars, mutual advising of students, and frequent collaboration on research projects. The academic interests of the finance faculty also span a very broad range of topics in finance, from the role of culture and trust in financial markets to the identification of jump risk premiums. The breadth of knowledge and interests of our faculty create an environment that encourages students to conduct advanced research in novel aspects of the field.  

Active Research Areas :  Current theoretical and empirical research in Finance spans the areas of asset pricing and corporate finance. Research topics include corporate governance, household financial decisions, macro-finance, financial crises, the pricing of securities in financial markets, international finance, financial history, development economics, market microstructure, regulation, and financial econometrics. Please note: Applicants to economics-based PhD programs, such as Finance, may opt-in to have their application considered by Weinberg's Economics PhD program. More information about this option is available on The Graduate School website . 

Finance faculty members include scholars who are fellows of the American Academy of Arts and Sciences, the National Bureau of Economics Research, and the Society for Financial Econometrics, as well as recipients of the Smith Breeden Prize from the American Finance Association and other top paper awards. Several faculty serve/served in editorial positions at leading journals, such as the Journal of Finance, Journal of Monetary Economics, and Econometrica , and as directors of the American Finance Association and past-presidents of the Western Finance Association. Recent publications within top economics and finance journals include American Economic Review , Econometrica , Journal of Finance , Journal of Financial Economics, and Journal of Political Economy.

What We Are Looking for in Applicants

We seek students with strong training in mathematics and statistics and a solid background in economics, either through prior study or through work and research experience. Recommended coursework at an advanced level includes calculus, linear algebra, optimization, probability and statistics. Although a master’s degree is not required, about half of our incoming class has a graduate degree. Prior research experience is not required.

Program Requirements

In years one and two, students take three or four courses each quarter (fall, winter, spring). The first-year students complete the three core sequences in Microeconomics, Macroeconomics and Econometrics. In year two, students enroll in the 3-course sequences in asset pricing and corporate finance, plus an additional course/elective – preferably from the Economics Department. Students must maintain a minimum 3.0 grade point average (GPA). Qualifying Exam At the end of year one, students are required to establish competence in the Economics course sequences: Microeconomics, Macroeconomics and Econometrics. This competence is satisfied by achieving a 3.0 grade point average (GPA) across the nine required courses in the sequence.

During the summer following the student’s second year of study, students must pass a comprehensive qualifying exam designed to measure competence in both asset pricing and corporate finance or they must demonstrate competence by maintaining a 3.6 GPA average across both course sequences.

Candidacy As students transition from coursework to research, they are required to write an original research paper in the summer of their second year supervised by a faculty advisor. Students present their completed research project to the department in September following the summer quarter of their second year. At that time their performance is reviewed by the Finance faculty, and upon successfully completing their coursework, passing their qualifying exam and second-year paper, students are admitted to candidacy.

Fourth Year Paper At the end of the fall quarter of the fourth year, students are required to pass the dissertation proposal requirement by presenting a completed research paper to the department. The research paper has to be sufficiently advanced to be part of the student's dissertation. Students who do not pass the dissertation proposal at that stage have an additional opportunity to do so by the end of the spring quarter of the fourth year.

Research, Proposal & Dissertation The main activity in years three and four is research toward a thesis of publishable quality, under the direction of one or more faculty advisors. During the third year, students are required to present their work in progress to the department. A thesis proposal must be presented to the Finance faculty by the end of fall quarter of their fourth year. In their final year in the program, each candidate must complete a dissertation demonstrating original and significant research and must pass a final oral examination (“defense”) on the dissertation.

Teaching Requirement To promote engagement with faculty and integration with the intellectual life of the department, students serve as research assistants and teaching assistants during years two, three, and four. Research assistantships (RAs) are an excellent lead-in to research; teaching assistantships (TAs) prepare students for teaching after obtaining the PhD.

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The Mathematical and Computational Finance Program at Stanford University (“MCF”) is one of the oldest and most established programs of its kind in the world. Starting out in the late 1990’s as an interdisciplinary financial mathematics research group, at a time when “quants” started having a greater impact on finance in particular, the program formally admitted masters students starting in 1999. The current MCF program was relaunched under the auspices of the Institute for Computational and Mathematical Engineering in the Stanford School of Engineering in 2014 to better align with changes in industry and to broaden into areas of financial technology in particular. We are excited to remain at the cutting edge of innovation in finance while carrying on our long tradition of excellence.

The MCF Program is designed to have smaller cohorts of exceptional students with diverse interests and viewpoints, and prepare them for impactful roles in finance. We are characterized by our cutting edge curriculum marrying traditional financial mathematics and core fundamentals, with an innovative technical spirit unique to Stanford with preparation in software engineering, data science and machine learning as well as the hands-on practical coursework which is the hallmark skill-set for leaders in present day finance.

Mathematics (PHD) – Financial Mathematics Track

Program at a glance.

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The Financial Mathematics track in the Mathematics PhD program is designed to prepare students for research and leadership positions in industry, government, non-governmental organizations, and academia requiring employment of financial mathematics.

The Mathematics PhD program consists of at least 75 credit hours of course work beyond the bachelor's degree, of which a minimum of 48 hours of formal course work, exclusive of independent study, are required. The program requires 36 credit hours of core courses and 15 credit hours of dissertation research (7980).

Total Credit Hours Required: 75 Credit Hours Minimum beyond the Bachelor's Degree

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Enter your information below to receive more information about the Mathematics (PHD) – Financial Mathematics Track program offered at UCF.

Track Prerequisites

Bachelor's degree in related field.

Students entering the graduate program with regular status are assumed to have a working knowledge of undergraduate calculus, differential equations, linear algebra (or matrix theory), boundary value problems, statistics, computer programming, and maturity in the language of advanced calculus (at the level of MAA 4226).

Degree Requirements

Required courses.

• All students are required to complete the following courses with grade of "B" or better.
• MAA5237 - Mathematical Analysis (3)
• MAS5145 - Advanced Linear Algebra and Matrix Theory (3)
• MAP5641 - Financial Mathematics I (3)
• MAP6642 - Financial Mathematics II (3)
• MAP5612 - Computational Methods for Financial Mathematics I (3)
• MAP6616 - Computational Methods for Financial Mathematics II (3)
• MAP6646 - Risk Management for Financial Mathematics (3)
• MAP5606 - Differential Equations for Financial Mathematics (3)
• MAP6195 - Mathematical Foundations for Massive Data Modeling and Analysis (3)
• MAP6207 - Optimization Theory (3)
• STA6857 - Applied Time Series Analysis (3)
• MAP5931 - Proseminar for Financial Mathematics (1)
• MAP5933 - Seminar in Financial Mathematics (2)
• The remaining credit hours consist of additional dissertation research (7980 or 7919), at least 15 credit hours of regular classroom elective courses, and at most 12 credit hours of independent study or independent directed research. Students who pass the qualifying examination may substitute some of the core courses with the approval of the adviser and the graduate program director.

Elective Courses

• Earn at least 24 credits from the following types of courses: Elective courses require the approval of the adviser and the graduate program director; up to 12 credit hours of elective courses may be taken outside the department. At least one-half of the program courses must be taken at the 6000 level. At least 12 hours of elective course work must be formal course work, exclusive of independent study. Electives are chosen in consultation with the student's advisory committee and may be chosen from the suggested options: Discrete Mathematics, General Applied Mathematics, Mathematical Computer Tomography, Image Processing and Computer Graphics, Mathematical Finance, Mathematical Physics, Pure Mathematics, Data Science, and Mathematical Statistics. A list of elective course options can be obtained from the graduate program director. Courses that are taken outside the Mathematics department must be approved by both the adviser and graduate program director. These courses are selected in consultation with the student's advisory committee.

Dissertation

• Earn at least 15 credits from the following types of courses: MAP 7980 - Dissertation Research 15 Credit Hours (minimum) After passing the candidacy examination and meeting the other requirements that are required for admission to candidacy, the student can register for Doctoral Dissertation (MAP 7980). A minimum of 15 Doctoral Dissertation credit hours are required for the degree.

Examinations

Qualifying examination.

• The qualifying/comprehensive examination is based on the core course work. To continue in the PhD program, students must pass the examination at the PhD level. Two attempts are permitted. The examination will be administered twice a year: one in the Fall semester and the other in the Spring semester. To take the examination, students must have earned a "B" or better in each core course, must have a minimum grade point average of 3.0 (out of 4.0) in the program, or must obtain permission from the graduate program director. Students will normally take the examination after the first year and are expected to have passed it by the end of the second year of study, unless a written request for a postponement has been approved by the Graduate Committee at least two months before the examination date. The student must pass the Qualifying Examination in at most two attempts. It is strongly recommended that the student select a dissertation adviser by the completion of 18 credit hours of course work, and it is strongly recommended that the student works with the dissertation adviser to form a dissertation committee within two semesters of passing the Qualifying Examination.

Candidacy Examination

• The Candidacy Examination consists of a written examination based on the materials from two selected two-semester sequence courses taken by the students. A committee formed or selected by the Graduate Committee or the graduate program director is responsible for preparing and grading the written examinations. Each sequence that is selected for the candidacy examination must be approved by the dissertation adviser, the dissertation committee, and the graduate program director. Students in the Financial Mathematics Track will ordinarily select one of the sequences for their candidacy examination to be MAP 5641/MAP6642 Financial Mathematics I and II, and MAP5612/MAP6616 Computational Methods for Financial Mathematics I and II. The Candidacy Examination can be attempted after passing the qualifying examination. The Candidacy Examination must be completed within three years after passing the qualifying examination. A student must successfully pass the Candidacy Examination within at most two attempts.

Admission to Candidacy

• The following are required to be admitted to candidacy and enroll in dissertation hours: Completion of all course work, except for dissertation hours. Successful completion of the candidacy examination. The dissertation advisory committee is formed, consisting of approved graduate faculty and graduate faculty scholars. Submittal of an approved program of study.

Dissertation Proposal Examination

• After passing the candidacy examination, the student will prepare a dissertation proposal and orally present it to the dissertation advisory committee for approval. The proposal will include a description of the research performed to date and an agenda for the research planned to be completed for the dissertation. In addition to standards of correctness, indicating a suitable level of mastery of the material of the area of the dissertation, and suitability of the proposed dissertation topic, the presentation must meet current standards for professional presentations within the discipline of mathematics. For the successful completion of the Dissertation Proposal Examination, the presentation must be judged as passing the requirements for the examination by the majority of the dissertation committee. This exam must be passed within 18 months of passing the candidacy examination and not later than the end of the sixth year of graduate study. A candidate must pass this examination within at most two attempts.

Dissertation Defense

• Upon completion of a student's research, the student's committee schedules an oral defense of the dissertation. Most students complete the program within five years after obtaining their bachelor's degree. Students are expected to complete the dissertation in no more than seven years from the date of admission to the program.

Independent Learning

• The required 15 credit hours of dissertation will provide ample opportunities for students to gain the independent learning experience through studying published research papers and deriving, on their own, new and meaningful research results.

Grand Total Credits: 75

Application requirements, financial information.

Graduate students may receive financial assistance through fellowships, assistantships, tuition support, or loans. For more information, see the College of Graduate Studies Funding website, which describes the types of financial assistance available at UCF and provides general guidance in planning your graduate finances. The Financial Information section of the Graduate Catalog is another key resource.

Fellowship Information

Fellowships are awarded based on academic merit to highly qualified students. They are paid to students through the Office of Student Financial Assistance, based on instructions provided by the College of Graduate Studies. Fellowships are given to support a student's graduate study and do not have a work obligation. For more information, see UCF Graduate Fellowships, which includes descriptions of university fellowships and what you should do to be considered for a fellowship.

The department offers over 20 Graduate Teaching Assistantships every year on a competitive basis. A few Graduate Research Assistantships are also available for qualified students.

Finance Requirements

The PhD finance concentration requires a strong mastery of economic theory. Students spend the first year taking a doctoral-level sequence in microeconomic theory and a sequence in econometric analysis. They are also required to take four, two-credit finance PhD seminars in the first year. The program encourages students with a more limited technical background to select appropriate courses in mathematics or statistics, and students with no previous finance coursework are encouraged to audit MBA program finance courses

In the second year, coursework includes doctoral seminars on current topics in finance along with elective courses generally in accounting, economics, or mathematics. Some students, depending on their course of study, may take the microeconomics written preliminary examination at the end of their first year.

Students also write summer papers at the end of their first and second year of coursework and complete the finance written preliminary examination at the end of their second year. Students who successfully complete their summer papers and pass the written and oral preliminary exams begin work on a dissertation leading to the PhD in Business Administration.

Students are required to complete all finance PhD seminars offered plus an additional 8 credits of required ECON coursework: either the Econ 8001-04 sequence or the Econ 8101-04 sequence for a total of at least 24 major field credits. Students must also complete a minimum of 16 additional credits of supporting field coursework in areas such as economics, statistics, and accounting, for a total of at least 40 credits of degree program coursework to progress to the prelim exams.

Course descriptions:

Fina 8802: Theory of Capital Markets I: Discrete Time

The course covers the essentials of modern asset pricing theory using static and discrete time frameworks. The fundamental asset pricing equation is introduced that uses the stochastic discount factor to price securities. The course develops a general approach that is then used to examine several classical models in finance-CAPM, consumption-based CAPM, and the APT. The course also introduces students to essential concepts of complete markets, representative agent and Pareto optimality. Some of the advanced topics discussed include overview of the present challenges to the theories and some modern approaches such as habit formation and heterogeneous agents (incomplete markets) model.

Fina 8803: Theory of Capital Markets II: Continuous Time

This course is an introduction to the theory of continuous- time financial economics. The emphasis is on the main mathematical and statistical tools on which the theory is built. Course content includes Ito processes, Girsanov’s theorem, and risk-neutral pricing. Upon completion of the course, students should be sufficiently familiar with these tools to be able to formulate and analyze continuous-time models.

Fina 8804: Advance Continuous Time Finance

This course continues where Fina 8803 ended. Some of the topics investigated include the pricing of fixed income securities, optimal capital structure, and general equilibrium. From there, classic papers in this field will be read and replicated by the students.

Fina 8810 : Topics in Asset Pricing  This course investigate current topics in the asset pricing literature. The goal is to have students read these papers, rederive the main results, identify the main assumptions, and thus identify ideas on how to improve upon the current literature.

Fina 8812: Corporate Finance I

This course covers theoretical work in four major areas of corporate finance: corporate control, managerial incentives, corporate governance, and capital structure. The perspective taken is that understanding corporate finance decisions is impossible without a solid understanding of the theory of the firm-what assets are collected within the firm and what determines the boundaries of the firm. Empirical evidence in support of theoretical models is also discussed. The course will begin with a review of modern theories of the firm based on incomplete contracts. Each of the subsequent topics will then show how corporate finance decisions either expand or limit the scope of the firm.

Fina 8813: Corporate Finance II

This course covers varied topics in theoretical corporate finance like initial public offering, dividend policy, financial distress and its resolution, financial intermediation and applications of auctions in finance. The course will also cover some topics in market microstructure.

Fina 8820: Topics in Corporate Finance

This readings course will focus on recent contributions in corporate finance. Goal is to produce ideas for new research. Course offered yearly, alternating between theory and empirics.

Fina 8822: Empirical Methods in Finance

This course will introduce students to many of the empirical methods used in modern financial economics. The course focuses on the empirical techniques used most often in the analysis of financial markets and how they are applied to actual market data. The list of topics includes: a) statistical properties of asset returns and the efficient markets hypothesis, b) empirical tests of asset pricing models (CAPM, APT, Intertemporal CAPM, Consumption CAPM), c) tests of conditional asset pricing models, and d) other relevant topics.

Fina 8823: Empirical Corporate Finance

The course focuses on current empirical research on corporate finance, mergers/acquisitions, equity offerings, event studies, tests of market efficiency, impact of corp. governance, etc.

Fina 8890: Seminar: Finance Topics

Topics vary.

First year students will be tested on two intro and two intermediate courses that have been taken during their first year. Students must take and pass this exam in the summer between their 1st and 2nd years in the program. A retake of this exam may be permitted, pending department approval. Those who retake the exam must pass it before the end of their 2nd year in the program. Failing this exam twice will result in the student’s removal from the program.

Students are expected to work on research during the summer. Their 1st summer paper is due by Sept. 15th of the 2nd year. The goal of the 1st summer paper is to get the students started on independent research. The topic and the scope of the paper must be approved by the PhD coordinator in consultation with the student’s adviser. The requirements for the 2nd summer paper are more stringent. It should be original research. The 1st draft of the paper is due on Sept. 15 of the 3rd year. To satisfactorily meet the requirement, the paper has to be approved by 2 readers and the presentation has to be deemed satisfactory by the department’s faculty. Students are expected to incorporate feedback and submit the final draft by Dec. 15th of the 3rd year. After the final draft is turned in, students can progress to the oral exam, which is based on this research paper.

Second year students will be tested on the two intermediate courses taught in their second year. Students will take the written exam in early summer after completion of the second year. Though subject to change, the exam is usually given over a series of days during a 2-week time period in June.

The oral exam is often based on the summer research paper that students complete by the beginning of their 3rd year in the program, though this format is not mandatory. The exam will normally occur during spring semester of the student's third year.

Should be completed in spring semester of the fourth year.

In the third and the fourth years, students will independently teach 3 credits per year. The timing of the courses can be adjusted depending on departmental need.

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Department of Mathematics

Financial mathematics.

A pioneer in its field, the Financial Mathematics Program offers 15 months of accelerated, integrated coursework that explores the deep-rooted relationship that exists between theoretical and applied mathematics and the ever-evolving world of finance. Their mission is to equip students with a solid foundation in mathematics, and in doing so provide them with practical knowledge that they can successfully apply to complicated financial models. Financial Mathematics students become leaders in their field; program alumni have gone forth to find success at companies like JP Morgan, UBS, and Goldman Sachs. Read more

To apply for admissions and financial aid, or for additional information on admissions requirements for the Ph.D. program in pure mathematics, please go to the appropriate Harvard Kenneth C. Griffin Graduate School of Arts and Sciences website listed below. All other inquiries may be directed to the Graduate Program Administrator of the Mathematics Department.

• Harvard Kenneth C. Griffin Graduate School of Arts and Sciences (Harvard Griffin GSAS)
• Mathematics Graduate Studies
• Financial Support

Graduate Program Administrator

The Department of Mathematics does not discriminate against applicants or students on the basis of race, color, national origin, ancestry or any other protected classification.

Preparing the Application The statement of purpose for graduate applications is carefully weighted by the admissions committee. The applicant’s statement should convince the committee that they are able to communicate effectively and with a deep understanding of mathematics. It is not intended to be a biographical sketch or a reflection on one’s decision to enter the field.

Three letters of recommendation are required. Letter writers should be faculty or others qualified to evaluate the applicant’s potential for graduate study in mathematics. The letters must be submitted online and by the application deadline.

Applicants should include any research papers, publications, and other original works they would like to have evaluated by the admissions committee.

The department requests that applicants submit GRE Mathematics Subject Test scores if practical. Applicants should check on the ETS website for test dates in their area to ensure the scores will be submitted before the application deadline. An official score report should be sent to Harvard Kenneth C. Griffin Graduate School of Arts and Sciences using code 3451.

While the admissions committee reviews all applications submitted before the deadline, missing math subject test scores provide one less data point available to evaluate the application. Depending on the strength of the application, the missing subject test scores may put the application at a disadvantage.

Applicants who are non-native English speakers and who do not hold an undergraduate degree from an institution at which English is the primary language of instruction must submit scores from the Internet Based Test (IBT) of the Test of English as a Foreign Language (TOEFL) or the International English Language Testing System (IELTS) Academic test.

Harvard Griffin GSAS requires applicants to upload an electronic copy of undergraduate transcripts. Hard copies of official transcripts are not required at the time of application.

Ph.D. Program in Pure Mathematics The department does not grant a terminal Master’s degree, but the Master’s can be obtained “on the way” to the Ph.D. by fulfilling certain course and language exam requirements.

In general, there is no transfer status application to the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences or to the Department of Mathematics. No formal credit is given for an MSc or MA earned elsewhere. All applicants are considered to be applying as first-year graduate students. The only difference Master’s study may make is to better prepare students for the Qualifying Exam.

All graduate students are admitted to begin their studies in the fall term. The department plans on an entering class of about twelve students. Since the admissions committee receives a few hundred applications, the competition is keen.

Funding Graduate Study Applicants are urged to apply for all funding available to them. If no outside funding is available to the applicant, financial aid in the form of scholarships, research assistantships, and teaching fellowships is available. In general, students who do not have outside support will get scholarship support in their first year, but students are required to act as a teaching fellow for one-half course (i.e. for a one-term course) in their second through fifth years.

The department strongly recommends applicants to seek out and apply for all sources of financing available to them for graduate study. Recommended sources for funding US graduate students are NSF Graduate Fellowships and NDSEG Fellowships . Applicants from the UK are urged to also apply for the Kennedy fellowships and applicants from UK, New Zealand, Canada and Australia for Knox fellowships . International students may apply for the Fullbright IIE or any home country fellowships available for study abroad.

Harvard John A. Paulson School of Engineering and Applied Sciences The Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) offers programs for both the Master’s degree and the Ph.D. degree in Applied Mathematics. Please visit the SEAS website for more information on degrees in applied mathematics at www.seas.harvard.edu

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Finance Phd Math Requirements.

By Osondi July 28, 2010 in PhD in Business

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I would love to know what the actual math requirements are in order to be able to cope with the coursework in a finance Phd program.

The reason i ask is that i have only one semester's worth of calculus during undergrad (2 if you count that joke that is called Applied Calculus for business majors). I would have taken Cal II but i was about to graduate and didn't have the time.

I have been accepted into a Masters in finance program and was going to use that opportunity to take more math courses to buttress my quant background. Willl this be possible?

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Thought I would share my experience here because I was in a similar situation as you on math background about 6 years ago... now starting a PhD Finance this fall. I had very little calculus from undergrad (like you, just Calc I) and a few other random math courses like math modeling, etc, but no linear algebra, real analysis, diff. eq, almost nothing on the standard list of these "required" courses. I did have lots of stats and econometrics as an undergrad, including an econometrics course at the graduate level. Not until my master's in econ though did I really start to really learn relevant math skills, through advanced econ theory, more econometrics, econ math courses, and independent textbook study. In the years since my master's, I have taken several upper-level grad probability and stats courses. Taken with other parts of my application, my math/stats background combined seemed to be acceptable for admissions purposes in the top 20 or so range.

Moral of the story is that you can overcome a thin undergrad math background. Obviously, beef up your math record as much as you can during your master's. I suspect you will need to work VERY hard as I did to catch up to your peers who have a stronger math background going into your master's program. I would also recommend taking advanced microecon theory, if not already required, because it will show that you can make it through some of the critical first year core coursework in a PhD finance program.

genericname

You need math in Finance PhD for two reasons.

First you need math courses on your transcript to be a competitive candidate for admission.

Second, as you mentioned, to facilitate your understanding of course materials in the PhD program.

Math requirement these days for admission purposes is very high. When other candidates will have many advanced math courses on their transcripts, you would not want to look light-weight candidate on the math side. From admission point of view, you need Calculus I, Calculus II, Calculus III and Linear Algebra at the minimum. Advanced math courses such as Probability Theory, Differential Equations, Real Analysis, and Stochastic Processes will further decorate your credentials in the admission process. When I started my masters program as a stepping stone for finance PhD, I had nothing but College Algebra and Trigonometry on my transcripts. I ended up taking all the math courses that I mentioned above during my masters program. So selection of masters program is important-- you need the flexibility to accomodate undergrad level courses in addition to the masters program courses.

After getting into the doctoral program, your math requirement will depend on the sort of work you choose to do for your research. For theoretical research, you will need to be a heavy-weight on math. For empirical research, Calculus I-III, Linear Algebra and Probability Theory will be enough to get through the econometrics courses initially. But if you want to come up with your own econometric model to approach your research problem, you are back to the requirement of solid math understanding.

Your ultimate math requirement will depend on the level of schools that you are shooting for. For top level schools, math are needed in the first place to get into and then you will need a solid understanding of math concepts to handle the top level research that you are expected to do while in school.

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Master of Financial Mathematics

UQ’s Master of Financial Mathematics is designed to equip you with sophisticated mathematical and computational techniques to measure and manage risk in the financial marketplace.

You'll study the pricing of financial contracts such as financial and real options, management of investment portfolios, capital adequacy requirements for financial institutions, valuation of firms, optimal capital management and optimal contracting.

The program offers you a practical and flexible curriculum that you can tailor to your interests and career goals through a range of elective courses, including Computation in Financial Mathematics, Financial Calculus, Machine Learning, Financial Risk Management, and Econometrics of Financial Markets.

You'll also be able to experience financial markets first-hand with an industry placement project, applying your knowledge and skills while working in sectors such as banking, energy trading or superannuation.

With a Master of Financial Mathematics qualification from UQ you’ll be highly sought after by investment banks, corporate risk management units, insurance companies, fund management institutions, financial regulatory bodies, brokerage firms and trading companies.

Program highlights

• Learn cutting-edge computational methodology, mathematical modelling and stochastic methods in finance to identify strategic investment or business opportunities, manage portfolios and price financial products.
• Benefit from UQ’s strong connections with industry and government and experience the financial markets first-hand with an industry placement.
• Build on your background in mathematics, commerce or economics/econometrics.

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61 in the world for accounting and finance

How you'll learn

Your learning experiences are designed to best suit the learning outcomes of the courses you choose.

• Work placements
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What you'll study

At UQ, degrees are called 'programs' and subjects are called 'courses'. Here's a sample of the courses you could study in this program:

• Introduction to Software Engineering
• Calculus and Linear Algebra I
• Mathematical Probability
• Financial Mathematics

See courses and program structure

Career possibilities

Postgraduate study can take you anywhere. Here are some of the careers you could be on your way to:

• Investment banker
• Retail banker
• Market risk manager
• Financial planning manager
• Data scientist
• Quantitative analyst
• Financial product developer
• Credit risk analyst
• Revenue manager
• Stockbroker

Graduate salary

Science and mathematics (postgraduate)

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I was fortunate to conduct my industry research project at Suncorp Group, where I applied the techniques I was learning in the classroom to develop machine-learning models to assess retail credit risk. UQ has lots of opportunities for students to meet and network.

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Entry requirements

It's possible to complete this degree in 2 years or 1.5 years depending on your qualifications and experience.

You can apply for any duration as long as you meet the entry requirements. You may also be eligible to apply for credit or exemptions to shorten your degree further. You'll graduate with the same qualification no matter how long you take to complete the degree.

2-year degree (32 units of study)

To be eligible to complete the degree in 2 years full-time (or part-time equivalent) full-time (only available as full-time study) , you'll need:

• a bachelor's degree (or equivalent) in any discipline with first-year, university-level mathematics (including single-variable and multi-variable calculus, ordinary differential equations, and linear algebra), or
• a graduate diploma (or equivalent) in financial mathematics, or
• to have successfully completed 3 years of study towards an approved qualification at an overseas partner institution, with a formal pathway to the Master of Financial Mathematics.

You must have a grade point average (GPA) of 5.0 on a 7-point scale in your previous qualification.

1.5-year degree (24 units of study)

If you have relevant prior learning or experience, you can reduce the number of courses you need to complete and graduate in less time.

To be eligible to complete the degree in 1.5 years full-time (or part-time equivalent) full-time (only available as full-time study) , you'll need:

• a bachelor's degree (or equivalent) in mathematics, or
• a bachelor's degree (or equivalent) majoring in mathematics.

GPA equivalent

Select where you studied and your qualification to see the GPA equivalent you need to be considered for this program.

Use the GPA equivalent as a guide. When you apply, we’ll calculate your GPA using the UQ grading scale. Any failing grades will be included. Entry requirements are subject to change.

Equivalent subjects

Related programs.

Depending on your previous qualifications and current goals, you might want to consider one of these related programs:

• Graduate Diploma in Financial Mathematics

English language requirements

IELTS overall 6.5; reading 6; writing 6; speaking 6; listening 6. For other English Language Proficiency Tests and Scores approved for UQ

TOEFL iBT (including Paper Edition) - Overall 87, listening 19, reading 19, writing 21 and speaking 19.

PTE Academic - Overall Score of 64 and 60 in all sub bands.

BE - A minimum overall grade of 4 plus a minimum grade of C in all macro skills.

CES - Overall 176 and 169 in all sub bands.

OET is not accepted.

There are other ways to meet the English language requirements. For some programs, additional conditions apply.

Learn how to meet the English language requirements

Student visas

International students who are accepted into full-time study in the Master of Financial Mathematics are eligible to apply for an Australian student visa (subclass 500).

There are a number of requirements you must satisfy before a visa is granted, including the Genuine Student (GS) requirement.

Learn more about student visas

Fees and Scholarships

Indicative annual fee.

Approximate yearly cost of tuition (16 units). Your fees will vary according to your selected courses and study load. Fees are reviewed each year and may increase.

Fee information for 2025 is not yet available. Fee information displayed is for 2024.

Learn more about postgraduate fees

Approximate yearly cost of full-time tuition (16 units). Your fees will vary according to your study load. Fees are reviewed each year and may increase.

AUD $50,560

Government assistance, financial aid.

As an international student, you might be eligible for financial aid – either from your home country, or from the Australian Government.

Learn more about financial aid

Domestic places in the Master of Financial Mathematics are Commonwealth Supported. This means the cost of your education is shared between you and the Australian Government.

Instead of tuition fees, Commonwealth Supported students pay what are called student contribution amounts.

HECS-HELP is an Australian Government loan scheme to assist eligible students with the cost of their student contribution amounts.

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The Australian Government offers a number of income-support payments to eligible Australian university students.

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You may be eligible for more than 100 scholarships, including:

Applying online

All international applications should be submitted to UQ. If you prefer, you can use an  approved UQ agent in your country .

The program code for the Master of Financial Mathematics is  5573 .

This program is available in multiple durations. You can apply for any duration as long as you meet the entry requirements.

When you apply, select your preferred duration. If you don't meet the requirements for your first preference, we'll automatically consider you for entry into a longer duration.

Find out more about applying for postgraduate coursework study

All domestic applications should be submitted to UQ.

The program code for the Master of Financial Mathematics is 5573 .

When you apply, select your preferred duration. You can also ask us to consider you for a longer duration if you don't meet the entry requirements for your first preference.

Important dates

The closing date for this program is:

• To commence study in semester 2 - May 31 of the year of commencement.
• To commence study in semester 1 - November 30 of the previous year.

To learn more about UQ dates, including semester start dates, view the Academic Calendar .

• To commence study in Semester 1 - January 31 of the year of commencement.
• To commence study in Semester 2 - June 30 of the year of commencement.

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