Before revision: 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.
After revision: This article studies 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.