Portfolio Optimization & Option Pricing in a Component-wise Semi-Markov Modulated Market

Abstract

This thesis studies three problems of mathematical finance. We address the appropriateness of the use of semi-Markov regime switching geometric Brownian motion (GBM) to model risky assets using a statistical technique. Component-wise semi-Markov (CSM) process is a further generalization of the semi-Markov process, which becomes relevant when multiple assets are under consideration. In this thesis, we would present the solution to the optimization problem of portfolio-value, consisting of several stocks under risk-sensitive criterion in a component-wise semi-Markov regime-switching jump diffusion market. Finally, the solution to locally risk minimizing pricing of a broad class of European style basket options would be demonstrated under a market assumption where the risky asset prices follow CSM modulated time inhomogeneous geometric Brownian motion.