IE 592 Special Topics: Stochastic Models in Finance

An introduction to stochastic models in financial decision making. Discrete time models: Martingales, risk-neutral probability measure and Radon-Nikodym derivative in discrete time. Brownian motion, Ito’s formula and change of measure in continuous time, along with the Black-Scholes model. Discussion on stopping times and their application to American options. Stochastic models for interest rates and fixed income derivatives.