PhD in Mathematical Finance Curriculum
The curriculum for the PhD in Mathematical Finance is tailored to each incoming student, based on his or her academic background. Typically, students will begin the program with a full course load to build a solid foundation in understanding not only math and finance but the interplay between them in the financial world. As technology plays an increasingly larger role in financial models, computer science 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 indepth research. It is also expected that doctoral students will perform teaching assistant duties, which may include lectures to master’slevel classes.
Sample Curriculum Guide
Year 1 FALL FIRST YEARGRS EC701 – MICROECONOMIC THEORY GRS EC702 – MACROECONOMIC THEORY GSM FE918 – DOCTORAL SEMINAR IN FINANCE GSM MF793 – STATISTICAL METHODS OF MATHEMATICAL
SPRING FIRST YEARGRS EC703 – ADVANCED MICROECONOMIC THEORY GRS EC704 – ADVANCED MACROECONOMIC THEORY GSM FE920 – ADVANCED CAPITAL MARKET THEORY GSM MF728 – FIXED INCOME SECURITIES

Year 2 FALL SECOND YEARGSM FE919 – ADVANCED DERIVATIVE SECURITIES GRS EC712 – ECONOMETRIC TIME SERIES GSM MF730 – PORTFOLIO THEORY GSM MF772 – CREDIT RISK
SPRING SECOND YEARGSM MF 796 – COMPUTATIONAL METHODS OF MATHEMATICAL FINANCE GRS EC744 – ECONOMIC DYNAMICS GSM MF921 – DYNAMIC ASSET PRICING WITH FRICTIONS GSM MF794 – STOCHASTIC OPTIMAL CONTROL AND INVESTMENT

Years 3, 4, & 5: Dissertation research* 
* Students typically take 45 years to complete the PhD program.
Prerequisites
Due to the highly quantitative nature of this program, incoming students are expected to have a strong mathematical background comparable to a PhD student in mathematics. To be considered for admission, all master’s and PhD applicants must have taken, at the minimum:
Calculus I: Limits; derivatives; differentiation of algebraic functions. Applications to maxima, minima, and convexity of functions. The definite integral, the fundamental theorem of integral calculus, and applications of integration.
Calculus II: Logarithmic, exponential, and trigonometric functions. Sequences and series, and Taylor’s series with the remainder. Methods of integration.
Calculus III: Vectors, lines, and planes. Multiple integration, and cylindrical and spherical coordinates. Partial derivatives, directional derivatives, scalar and vector fields, the gradient, potentials, approximation, multivariate minimization, Stokes’s, and related theorems.
Linear Algebra: Matrix algebra, solution of linear systems, determinants, Gaussian elimination, fundamental theory, and rowechelon form. Vector spaces, bases, and norms. Computer methods. Eigenvalues and eigenvectors, and canonical decomposition. Applications.
Differential Equations: Firstorder linear and separable equations. Secondorder equations and firstorder systems. Linear equations and linearization. Numerical and qualitative analysis. Laplace transforms. Applications and modeling of real phenomena throughout.
Basic computer programming skills.
Suggested Readings
 JP. Danthine and J.B. Donaldson, Intermediate Financial Theory, 2nd edition
 T.E. Copeland, J.F. Weston and K. Shastri, Financial Theory and Corporate Policy
 H. Varian, Intermediate Microeconomics
 R. Gallant, An Introduction to Econometric Theory
 D. Williams, Probability with Martingales
 M. Hoy , J. Livernois, C. McKenna, R. Rees, and T. Stengos, Mathematics for Economists