A0925
Title: Utility maximization in a continuous-time financial market: Filtering and uncertainty
Authors: Joern Sass - RPTU Kaiserslautern-Landau (Germany) [presenting]
Abstract: In financial markets, simple portfolio strategies often outperform more sophisticated optimized ones. For example, in a one-period setting the equal weight or 1/N-strategy often provides more stable results than mean-variance-optimal strategies. This is due to the estimation error for the mean and can be rigorously explained by showing that for increasing uncertainty on the means the equal weight strategy becomes optimal, which is due to its robustness. In earlier work, this result is extended to continuous-time strategies in a multivariate Black-Scholes-type market. To this end, optimal trading strategies are derived for maximizing the expected utility of terminal wealth under CRRA utility when having Knightian uncertainty on the drift, meaning that the only information is that the drift parameter lies in an uncertainty set. The investor takes this into account by considering the worst possible drift within this set. It is shown that indeed a uniform strategy is asymptotically optimal when uncertainty increases. The focus is on a financial market with a stochastic drift process and possibly uncertainty. The worst-case approach is combined with filtering techniques. In this setting, it is shown how an ellipsoidal uncertainty set can be defined based on the filters and it is demonstrated that investors need to choose a robust strategy to profit from additional information. Furthermore, possible extensions to uncertainty are discussed in both drift and volatility.
