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 in-depth research. It is also expected that doctoral students will perform teaching assistant duties, which may include lectures to master’s-level classes.

Sample Curriculum Guide

Year 1

FALL FIRST YEAR

GRS EC701 – MICROECONOMIC THEORY

GRS EC702 – MACROECONOMIC THEORY

GSM FE918 – DOCTORAL SEMINAR IN FINANCE

GSM MF793 – STATISTICAL  METHODS OF MATHEMATICAL

 

SPRING FIRST YEAR

GRS EC703 – ADVANCED MICROECONOMIC THEORY

GRS EC704 – ADVANCED MACROECONOMIC THEORY

GSM FE920 – ADVANCED CAPITAL MARKET THEORY

GSM MF728 – FIXED INCOME SECURITIES

 

Year 2

FALL SECOND YEAR

GSM FE919 – ADVANCED DERIVATIVE SECURITIES

GRS EC712 – ECONOMETRIC  TIME SERIES

GSM MF730 – PORTFOLIO THEORY

GSM MF772 – CREDIT RISK

 

SPRING SECOND YEAR

GSM 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 4-5 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 row-echelon form. Vector spaces, bases, and norms. Computer methods. Eigenvalues and eigenvectors, and canonical decomposition. Applications.

Differential Equations: First-order linear and separable equations. Second-order equations and first-order systems. Linear equations and linearization. Numerical and qualitative analysis. Laplace transforms. Applications and modeling of real phenomena throughout.

Basic computer programming skills.

Suggested Readings

  • J-P. 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