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Utility Maximization with Convex Constraints and Partial Information

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Abstract

We consider a market model where stock returns satisfy a stochastic differential equation with an unobservable, stochastic drift process. The investor’s objective is to maximize expected utility of terminal wealth, but investment decisions are based on the knowledge of the stock prices only. The performance of the resulting highly risky strategies can be improved considerably by imposing convex constraints covering e.g. short selling restrictions. Using filtering methods we transform the model to a model with full information. We provide a verification result and show how results on optimization under convex constraints can be used directly for a continuous time Markov chain model for the drift. In special cases we derive representations of the optimal trading strategies, including a stochastic volatility model.

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Authors and Affiliations

  1. RICAM, Austrian Academy of Sciences, Altenberger Str. 69, 4040, Linz, Austria

    Jörn Sass

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  1. Jörn Sass
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Correspondence to Jörn Sass.

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Supported by the Austrian Science Fund, FWF grant P17947-N12.

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Sass, J. Utility Maximization with Convex Constraints and Partial Information. Acta Appl Math 97, 221–238 (2007). https://doi.org/10.1007/s10440-007-9124-z

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  • DOI: https://doi.org/10.1007/s10440-007-9124-z

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