American Options, Supermartingales and Snell Envelope, Stopping Time, Decomposition of Supermartingales, 7. Continuous Time Model for Stock Prices, Brownian Motion, Continuous Martingale Stochastic Calculus, 8. Black-Scholes Differential Equation, The Market Price of Risk. I shall keep the prerequisites as small as possible, i.e., the course will be more of less self-contained. However, it is good to have exposure in probability and differential equations.
Finance is one of the fast growing areas in the corporate world.
Along with this, the explosion in financial instruments has led ot the development of new mathematical models and methods for their analysis. The course begins with a review of financial derivatives and their applications. Models of financial derivatives will be presented such as Black-Scholes model. The approach will be baseed on partial differential equations using analytic and numerical methods. Background in differential equations and introductory probability or consent of the instructor.