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

A. Gabih, J. Saß and R. Wunderlich

In: N.Kolev, P. Morettin (eds.): Proceedings of the Second Brazilian Confrerence: on Statistical Modelling in Insurance and Finance, Maresias, August 28 -- September 3, 2005, Institute of Mathematics and Statistics, University of Sao Paulo, 116--121, 2005.
Abstract :

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.