Optimal terminal wealth under partial information: Both the drift and the volatility driven by a discrete time Markov chain

We consider a multi-stock market model. The stock price process satisfies a stochastic differential equation where both the drift and the volatility are driven by a discrete-time Markov chain of finite states. Not only the underlying Brownian motion but also the Markov chain in the stochastic differential equation are assumed to be unobservable. Investors can observe the stock price process only. The main result of this paper is that we derive the approximation of the optimal trading strategy and the corresponding optimal expected utility function from terminal wealth.