Study of Various Stochastic Differential Equation Models for Finance

Abstract

The first part of the study focuses on European and American option pricing. We explore the jump diffusion models with stochastic volatility within the general equilibrium framework and use the minimal martingale measure as martingale measure. The second part of the thesis is on portfolio optimization. We formulate optimal asset allocation problem with multiple-periods under mean variance utility in the game theoretic framework, develop and solve a series of extended HJB equations for the problem.