Stochastic Control in Optimal Portfolio with Regime Switching Model

Portfolio stochastic control problem is proposed and analyzed for a market consisting of one bank account and multiple stocks. The market parameters, including the bank interest rate and the appreciation and volatility rates of the stocks, 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. This essentially renders the underlying market incomplete. A Markov chain modulated diffusion formulation is employed to model the problem. Using techniques of stochastic control theory and martingale optimality principle, a general verification theorem is obtained. Applying the verification theorem, the optimal control and value functions for the problems of utility maximization are derived explicitly.