Stochastic Calculus for Finance

3 credits · Graduate Programs

Martingales in discrete and continuous time, risk-neutral valuations, discrete- and continuous-time (B,S)-security markets, the Cox-Ross-Rubinstein formula, Wiener and Poisson processes, Itô's formula, stochastic differential equations, Girsanov's theorem, the Black-Scholes and Merton formulas, stopping times and American options, stochastic interest rates and their derivatives, energy and commodity models and derivatives, value-at-risk and risk management. Prerequisite(s): Admission to a graduate program in Mathematics and Statistics or consent of the Department. Antirequisite(s): Credit for Mathematics 681 and any one of Mathematics 581, Applied Mathematics 681, or Applied Mathematics 581 will not be allowed. Also known as: (formerly Applied Mathematics 681)