PDE for Finance

A class in Mathematics in Finance
Courant Institute of Mathematical Sciences,
New York University
Spring Semester, 2008


Jonathan Goodman
room 617 Warren Weaver Hall
office hours: 10 - 12 Wednesdays
          or by appointment

Teaching Assistant

Roger Chen
room 611 Warren Weaver Hall
office hours: 6 - 7 Wednesdays, 4 - 5 Fridays
          or by appointment


Mondays, 5:10 - 7 pm
1302 Warren Weaver Hall
Starting January 28

Course description

Partial differential equations are among the most important modeling and analysis tools in quantitative finance. This goals of the class are:

  • The theory of the partial differential equations most used in finance
  • The connection between partial differential equations and diffusion processes
  • Boundary conditions
  • Formulating partial differential equations that solve optimization problems --
    Hamilton Jacobi Bellman equations
  • Formulating and analyzing jump diffusion models
  • The Fourier transform and its application to finding special solutions
  • Perturbation theory and approximate solutions

Some target applications will be:

  • Pricing exotic options with barriers and lookback features
  • Explicit solutions of the Heston and Vasicek models
  • Merton’s optimal dynamic investment problem
  • The optimal liquidation model of Almgren and Chriss
  • Treating small factors by perturbation theory