EURO 2024 Copenhagen
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1083. Robust Utility Maximization in Continuous Time: Filtering for Shaping the Uncertainty Sets

Invited abstract in session MC-57: Dynamic portfolio selection: stochastic optimization, filtering, and learning techniques, stream Modern Decision Making in Finance and Insurance.

Monday, 12:30-14:00
Room: S06 (building: 101)

Authors (first author is the speaker)

1. Jörn Sass
Mathematics, RPTU Kaiserslautern-Landau

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. In earlier work, we extended this result to continuous-time strategies in a multivariate Black-Scholes type market. To this end we derived optimal trading strategies for maximizing 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 showed that indeed a uniform strategy is asymptotically optimal when uncertainty increases. In this talk we focus on a financial market with a stochastic drift process and possibly uncertainty. We combine the worst-case approach with filtering techniques by defining an ellipsoidal uncertainty set based on the filters. We demonstrate that investors need to choose a robust strategy to profit from additional information.

Keywords

Status: accepted

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