The Financial Mathematics track within the Mathematics Ph.D. program is a rigorous specialization that equips students with the expertise needed for research-intensive and leadership roles in academia, industry, government, and non-governmental organizations. With a strong focus on the mathematical foundations of finance, the program emphasizes the development of advanced models and techniques essential for tackling complex financial challenges. It is tailored for students passionate about theoretical mathematics and its applications in modern finance.
The curriculum provides an in-depth study of financial mathematics, covering key areas such as stochastic PDE, probability theory, optimization, and numerical methods. The program demands high mathematical rigor, ensuring students are well-prepared to conduct cutting-edge research and contribute innovative solutions in fields like: quantitative finance, risk management, and asset pricing.
Graduates of this mathematically intensive program are equipped to become thought leaders in financial mathematics, capable of addressing real-world challenges with sound, innovative approaches.
The Financial Mathematics track program consists of 72 credit hours beyond the bachelor’s degree, structured as follows:
- 57 credit hours of formal coursework:
- 30 credit hours from required courses focusing on core topics fundamental to financial mathematics.
- 27 credit hours from elective courses, allowing students to tailor their studies according to their research interests.
- 15 credit hours of dissertation research (MAT 7980).
Master en route is permitted and encouraged.
Total Credit Hours Required: 72 Credit Hours Minimum beyond the Bachelor's Degree
Track Prerequisites
Bachelor's degree in mathematics or related field.
Students admitted to the Financial Mathematics track with regular status are expected to possess a solid foundation in undergraduate mathematics, including the calculus sequence, differential equations, and linear algebra. Additionally, they should demonstrate proficiency in constructing and understanding mathematical proofs, exhibiting a level of mathematical maturity comparable to that attained in an Advanced Calculus course, such as UCF’s MAA 4226.
For students identified as having background deficiencies or lacking sufficient mathematical skills, the program offers remedial courses during the first semester, structed as split-level classes.
Degree Requirements
Required Courses
30 Total Credits
- Complete all of the following
- Complete the following:
- MAA5237 - Mathematical Analysis (3)
- MAS5145 - Advanced Linear Algebra and Matrix Theory (3)
- MAA5238 - Measure and Probability I (3)
- MAP5641 - Financial Mathematics I (3)
- MAP6642 - Financial Mathematics II (3)
- Complete at least 1 of the following:
- MAP5612 - Computational Methods for Financial Mathematics I (3)
- MAT5712 - Scientific Computing (3)
- Complete at least 1 of the following:
- MAP5606 - Differential Equations for Financial Mathematics (3)
- MAP5336 - Ordinary Differential Equations and Applications (3)
- Earn at least 9 credits from the following:
- MAP6616 - Computational Methods for Financial Mathematics II (3)
- MAP6646 - Risk Management for Financial Mathematics (3)
- MAP6195 - Mathematical Foundations for Massive Data Modeling and Analysis (3)
- MAP6197 - Mathematical Introduction to Deep Learning (3)
- MAP6207 - Optimization Theory (3)
- STA6857 - Applied Time Series Analysis (3)
- MAP6111 - Mathematical Statistics (3)
- ECO6281 - Financial Economics I: Asset Prices, Risk, and Information (3)
- ECO6282 - Financial Economics II: Continuous-Time Models (3)
- MAP5931 - Proseminar for Financial Mathematics (1)
- MAP5933 - Seminar in Financial Mathematics (2)
- MAP6356 - Partial Differential Equations (3)
Elective Courses
27 Total Credits
- Earn at least 27 credits from the following types of courses: After completing the required core courses, students must engage in elective coursework, earning a minimum of 27 credit hours. Elective courses must be selected with the approval of both the student’s advisor and the graduate program director to ensure alignment with the student’s academic and professional goals. While most electives should be completed within the Department of Mathematics, students may apply up to 9 credit hours from courses offered by other departments, provided these courses are not counted toward the core course requirements and have prior approval from the graduate program director. At least 50% of all program coursework must be at the 6000 level or higher. Additionally, students may apply up to 9 credit hours from independent study, directed research, or internships toward the elective requirement, but a minimum of 18 credit hours must consist of formal coursework. Electives are selected in close consultation with the student’s advisory committee and may include any advanced 6000 or 7000-level courses available through the general mathematics track. The complete list of approved elective course options can be obtained from the graduate program director. While internships are encouraged to provide practical experience, they are not mandatory for program completion. The following courses represent common elective options for students pursuing the Financial Mathematics track, providing a blend of advanced mathematical tools and financial applications: • MAP 6195 – Mathematical Foundations for Massive Data Modeling and Analysis (3) • MAP 6197 – Mathematical Introduction to Deep Learning (3) • MAP 6207 – Optimization Theory (3) • STA 6857 – Applied Time Series Analysis (3) • ECO 6281 – Financial Economics I: Asset Prices, Risk, and Information (3) • ECO 6282 – Financial Economics II: Continuous-Time Models (3) • MAA 6238 – Measure and Probability I (3) • MAA 6245 – Measure and Probability II (3) • MAP 6218 – Stochastic Calculus (3) • MAP 6111 – Mathematical Statistics (3) • MAP 6469 – Bayesian Analysis and Approximation Theory (3) • MAA 7239 – Asymptotic Methods in Mathematical Statistics (3) • MAA 6306 – Real Analysis (3) • MAA 6505 – Functional Analysis (3) • MAP 6385 – Applied Numerical Mathematics (3) • MAP 7386 – Numerical Solutions of Partial Differential Equations (3) • MAP 6387 – Numerical Linear Algebra (3)
Dissertation
15 Total Credits
- Earn at least 15 credits from the following types of courses: The dissertation is the cornerstone of the Ph.D. program—the ultimate objective and most critical component of the student’s academic journey. It must present a cohesive and well-structured narrative, including an introduction, literature review, methodology, results, and conclusions. It is expected to make a significant contribution to the student’s field of study, advancing knowledge or addressing key challenges within the discipline. The dissertation process concludes with an oral defense, where the student presents their work and responds to questions from the committee. Although not mandatory, students are strongly encouraged to submit articles based on their dissertation research to quality peer-reviewed journals before scheduling their defense. This demonstrates the relevance and impact of their work within the academic community. Students must complete a minimum of 15 credit hours in Dissertation Research (XXXX 7980), offering opportunities to develop independent research skills and contribute meaningfully to their field.
Examinations
0 Total Credits No Rules
Qualifying Examination
0 Total Credits
- Students in the Financial Math track are required to pass two written Qualifying Examinations, administered by the Graduate Program Committee with support from Mathematics Graduate Faculty. These examinations are intended to assess the student’s mathematical rigor and analytical maturity by testing foundational concepts in Analysis and Linear Algebra, corresponding to contents covered in MAA 5237 – Mathematical Analysis and MAS 5145 – Advanced Linear Algebra and Matrix Theory. The Qualifying Examinations are held twice yearly: just before the start of the Fall semester and at the beginning of the Spring semester. Eligibility to sit for the examination requires that students maintain a minimum program GPA of 3.0 on a 4.0 scale and submit a formal written request to take the examination at least thirty (30) days prior to the scheduled date. Students are expected to pass both qualifying examinations by the end of their first year. Passing both exams is required to continue in the program beyond the second year. Although there is no limit on the number of attempts allowed for students to take each exam, students who do not pass both exams by the end of their second year will be dismissed from the program but may be eligible for an MS degree en route.
Candidacy Examination
0 Total Credits
- The Candidacy Examination must be completed before a student’s formal admission to Ph.D. Candidacy. This examination emphasizes advanced topics aligned with the student’s prospective dissertation project, with a particular focus on research in financial mathematics. The exam is administered by the Candidacy Examination Committee, which consists of the student’s Ph.D. advisor and two additional members of the Graduate Faculty. It includes two distinct components: 1. Written Report – The student must submit a research report to the committee, which will assess the breadth, depth, rigor, and relevance of the work. The written report must demonstrate the student’s preparedness for independent research and alignment with their proposed dissertation topic in financial mathematics. 2. Oral Examination – Upon approval of the written report, the oral examination will be scheduled. This private exam provides an opportunity for the student to discuss their research report in depth. The examination committee will assess the student’s mastery of the presented material by asking questions related to the research topic contained in the approved written report. The structure and duration of the oral examination are determined by the Candidacy Examination Committee. The student is required to pass both components to advance in the program. A maximum of two attempts is permitted to successfully complete the examination. This rigorous process ensures that students are well-prepared to undertake their dissertation research and contribute novel insights to the field of financial mathematics. Students must complete the Candidacy Examination before the end of their fourth year. Students are granted a maximum of two attempts to successfully pass the examination. Students who do not pass the Candidacy Examination within two attempts and before the end of the fourth year will be dismissed from the program but may be eligible for an MS degree en route.
Seminar Participation
0 Total Credits
- Ph.D. students in the financial mathematics track are required to attend seminars and colloquia hosted by the Mathematics Department. Students in their third year and beyond are also expected to present their research or independent study annually.
Admission to Candidacy
0 Total Credits
- Admission to Candidacy marks a significant milestone in a Ph.D. student’s academic journey, signifying the successful completion of required coursework and examinations needed for independent research. This status represents a transition from coursework to original research, granting students greater independence and responsibility in their academic pursuits. It reflects faculty confidence in the student's readiness to contribute meaningfully to their field, paving the way for intensive research opportunities, leading to the successful completion of their dissertation, the pinnacle of their academic achievement. Requirements for Admission to Candidacy 1. Completion of Coursework: Students must complete all required coursework, maintaining a minimum program GPA of 3.0 on a 4.0 scale. This includes both foundational and advanced classes, totaling a minimum of 57 credit hours. Of these, at least 21 credit hours must be earned from courses at the 6000 and 7000 levels. 2. Candidacy Examination: Students must pass the Candidacy Examination, which, as described above, includes a written research report and an oral component. 3. Advisory Commitment: The dissertation advisory committee must be submitted and approved by the graduate program director. It consists of the PhD advisor, assisted by at least three other graduate faculties or scholars, with at least one of them external to the Department of Mathematics. 4. Program of Study: An approved program of study must be submitted. Once admitted to candidacy, students are expected to focus on their dissertation research.
Dissertation
0 Total Credits No Rules
Dissertation Proposal Examination
0 Total Credits
- After successfully passing the Candidacy Examination, the student is required to prepare a Dissertation Proposal and present it orally to the Dissertation Advisory Committee for approval. The proposal should comprehensively outline the research conducted to date, as well as provide a detailed agenda for the research intended to be completed for the dissertation. In addition to demonstrating a high level of mastery in the relevant area of study, the proposal must adhere to rigorous academic standards regarding correctness and the suitability of the proposed dissertation topic. The presentation must also meet the current standards for professional presentations within the discipline of mathematics. To successfully complete the Dissertation Proposal Examination, the presentation must be evaluated and judged as meeting the examination requirements by a majority of the Dissertation Committee. This examination must be completed within 12 months of passing the Candidacy Examination and no later than the end of the fifth year of graduate study. Furthermore, candidates are permitted a maximum of two attempts to pass this examination. Students who do not pass the Dissertation Proposal Examination within two attempts and before the end of the fifth year will be dismissed from the program but may be eligible for an MS degree en route.
Dissertation Defense
0 Total Credits
- Upon completion of the student's research, the Dissertation Advisory Committee will schedule an oral defense of the dissertation. This defense serves as a formal presentation in which the student articulates their research findings, methodology, and contributions to the field. The successful completion of the dissertation defense marks the culmination of the student's academic journey, demonstrating their preparedness to contribute original research to the academic community and/or to take on leadership roles in industry, government, or other sectors where advanced mathematical thinking is essential.
Independent Learning
0 Total Credits
- 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.
Time Limitation
0 Total Credits
- Most students are expected to complete their Ph.D. program within five years after joining the program. However, students are required to finalize their dissertation within a maximum of seven years after starting the program. This timeline ensures that students remain engaged with their research and maintain a trajectory towards timely graduation, while also providing adequate time to address any challenges that may arise during the dissertation process. Students who do not successfully defend their thesis by the end of the seventh year will be dismissed from the program but may be eligible for an MS degree en route. In exceptional cases, students may appeal for an extension to continue the program beyond the seventh year. For more information on UCF’s seven-year rule and the relevant forms, please refer to this link: https://graduate.ucf.edu/7-year-rule-completion-form/
Grand Total Credits: 72
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.
