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We consider a multi-stock market model where prices satisfy a stochastic differential equation with instantaneous rates of return modeled as a continuous time Markov chain with finitely many states. Partial observation means that only the prices are observable. For the investor’s objective of maximizing the expected utility of the terminal wealth we derive an explicit representation of the optimal trading strategy in terms of the unnormalized filter of the drift process, using HMM filtering results and Malliavin calculus. The optimal strategy can be determined numerically and parameters can be estimated using the EM algorithm. The results are applied to historical prices. Copyright Springer-Verlag Berlin/Heidelberg 2004Portfolio optimization, partial information, continuous time Markov chain, HMM filtering, stochastic interest rates,

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We apply the compactification method to study the control problem where the state is governed by an Ito stochastic differential equation allowing both classical and singular control. The problem is reformulated as a martingale problem on an appropriate canonical space after the relaxed form of the classical control is introduced. Under some mild continuity hypotheses on the data, it is shown by purely probabilistic arguments that an optimal control for the problem exists.The value function is shown to be Borel measurable.

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