Title: Convergence of optimal strategies in a continuous-time financial market with model uncertainty on the drift
Authors: Joern Sass - University of Kaiserslautern (Germany) [presenting]
Dorothee Westphal - TU Kaiserslautern (Germany)
Abstract: In financial markets, simple portfolio strategies often outperform more sophisticated optimized ones. E.g., 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. We extend this result to continuous-time strategies in a multivariate Black-Scholes-type market. To this end, we derive optimal trading strategies for maximizing the expected utility of terminal wealth under CRRA utility when we have 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. We show that a minimax theorem holds which enables us to find the worst-case drift and the optimal robust strategy quite explicitly. We derive the limits when uncertainty increases and show that a uniform strategy is asymptotically optimal. We also discuss a financial market with a stochastic drift process, combining the worst-case approach with filtering techniques. In this setting, we show how an ellipsoidal uncertainty set can be defined based on the filters, and we demonstrate that investors need to choose a robust strategy to profit from additional information.