A Continuous-time Utility Portfolio Selection in a market with Regime Switching

A continuous-time utility portfolio selection model is proposed and analyzed for a market consisting of one bank account and stock. The market parameters, including the bank interest rate and the appreciation and volatility rates of the stock, depend on the market mode that switches among a finite number of states, the random regime switching is assumed to be independent of the underlying Brownian motion, we construct an optimal portfolio using results from forward-backward stochastic differential equations theory. As an illustration, exact computation of the optimal strategy is done for the Logarithmic type utilities.