** Utility Maximization with Bounded Shortfall Risk
in an HMM for the Stock Returns
**

We consider a multi-stock market model where prices satisfy a stochastic differential equation with instantaneous rates of return modeled as an unobservable continuous time, finite state Markov chain. For investment decisions only the prices are available. Thus we have a hidden Markov model (HMM) for the stock returns. The investor wishes to maximize the expected utility of terminal wealth but under restrictions on the expected loss in utility compared to a benchmark. The optimal trading strategies can be expressed in terms of observable quantities.