Portfolio optimization and option pricing in a component wise semi markov modulated market

Abstract

This thesis studies three problems of mathematical finance We address the appropriatenessof the use of semi Markov regime switching geometric Brownian motion GBM tomodel risky assets using a statistical technique Component wise semi Markov CSM processis a further generalization of the semi Markov process which becomes relevant whenmultiple assets are under consideration In this thesis we would present the solution tothe optimization problem of portfolio value consisting of several stocks under risk sensitivecriterion 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 stylebasket options would be demonstrated under a market assumption where the risky assetprices follow CSM modulated time inhomogeneous geometric Brownian motion newline newline