IE 525

Credit: 2 hours.

Basic theory of stochastic differential equations and numerical techniques for their analysis with applications to financial modeling. Brownian motion, martingales, stochastic integration, Ito's formula, stochastic differential equations, partial differential equations, simulation methods for derivatives pricing, finite-difference techniques for Black-Scholes equations and options pricing, Monte Carlo methods, variance reduction techniques, and sensitivity calculations. May be repeated if topics vary to a maximum of 4 hours. Prerequisite: IE 523.