Financial Mathematics is concerned with designing and analyzing products that improve the efficiency of markets, and create mechanisms for reducing risk. This course develops quantitative methods for these goals: the notions of arbitrage and risk-neutral pricing in discrete time, specific models such as Black-Scholes and Heston in continuous time, and calibration to market data. Credit derivatives, the term structure of interest rates, and robust techniques in the context of volatility options will be discussed, as well as lessons from the financial crisis.
This course discusses the formulation and the solution techniques to a wide ranging class of optimal control problems through several illustrative examples from economics and engineering, including: Linear Quadratic Regulator, Kalman Filter, Merton Utility Maximization Problem, Optimal Dividend Payments, Contact Theory. The method of dynamic programming and Pontryagin maximum principle are outlined. Brief introductions to the general theory of backward and forward stochastic differential equations, related partial differential and viscosity theory are discussed again through the above... Read more about ORF 542, Stochastic Optimal Control