Abstract
This paper considers the optimal selection of portfolios for utility maximizing investors under a shortfall risk constraint for a financial market model with partial information on the drift parameter. It is known that without risk constraint the distribution of the optimal terminal wealth often is quite skew. In spite of its maximum expected utility there are high probabilities for values of the terminal wealth falling short a prescribed benchmark. This is an undesirable and unacceptable property e.g. from the viewpoint of a pension fund manager. While imposing a strict restriction to portfolio values above a benchmark leads to considerable decrease in the portfolio’s expected utility, it seems to be reasonable to allow shortfall and to restrict only some shortfall risk measure.
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