PDE for Finance

Course Details and Schedule

Lecture notes by Jonathan Goodman

  • Section 1, The Linear Heat Equation. Last update: January 29.
  • Section 2, The Fourier Transform and the Heat Equation. Last update: February 8.
  • Section 3, Theory. Last update: February 10.
  • Section 4, Solution techniques. Last update: February 25.
  • Section 5, Probability flux. Last update: March 3.
  • Section 6, Deterministic optimal control. Last update: March 28.
  • Section 7, More on deterministic optimal control. Last update: April 5.
  • Section 8, More on deterministic optimal control. very preliminary
  • Section 9, More on deterministic optimal control. very preliminary
  • Sample final exam,

Lecture notes by Bob Kohn

Books on PDE

  • Fritz John, Partial Differential Equations: A clear and concise reference for the linear heat equation with a down to earth treatment of qualitative properties such as existence, uniqueness, and regularity. It also covers Green's functions and Fourier transforms.

  • Lawrence C. Evans, Partial Differential Equations: A deeper and longer discussion of partial differential equations. It discusses nonlinear Hamilton Jacobi equations of the kind that arise in deterministic and stochastic control.

Books on finance

  • Robert Merton, Continuous Time Finance: A classic compilation of papers by Merton.

  • Silih Neftci, An Introduction to the Mathematics of Financial Derivatives: An intuitive and well illustrated elementary introduction to the relation between PDE and stochastic processes.

Books on stochastic calculus and PDE

  • Steven Shreve, Stochastic Calculus for Finance, II: A slow treatment of the relation between PDE and SDE.

  • J. Michael Steele, Stochastic Calculus and Financial Applications: A more careful mathematical treatment.

Deterministic and stochastic control

  • Michael Athans and P. L. Falb, Optimal Control: An Introduction to the Theory and Its Applications: A basic introduction to control theory that has derivations of the Hamilton Jacobi equations for optimal control problems.

  • Floyd Hanson Applied Optimal Control: A class page with helpful references and problems.

Page last updated: January 29, 2008