In the literature, researchers have widely addressed the portfolio optimization problem with various stock price models, and by choosing different kinds of optimization criteria. Models driven by Jump processes seem to provide a flexible class of models which capture statistical and economical properties of market data. In particular, we consider a portfolio optimization problem, without any consumption and transaction cost, where the market consisting of stock prices is modelled by a multi dimensional jump diffusion process with semi-Markov modulated coefficients. We study risk sensitive portfolio optimization on finite time horizon. We address the above mentioned problem by using a probabilistic approach to establish the existence and uniqueness of the classical solution of corresponding Hamilton-Jacobi-Bellman (HJB) equation. We also implement a numerical scheme to see the behavior of solutions for different values of initial portfolio wealth, maturity and risk of aversion parameter.
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