Title: Robust utility maximization in continuous-time financial markets
Authors: Dorothee Westphal - TU Kaiserslautern (Germany) [presenting]
Joern Sass - University of Kaiserslautern (Germany)
Abstract: Model uncertainty is a challenge that is inherent in many applications of mathematical models in various areas, for instance in mathematical finance and stochastic control. Robust strategies, i.e., strategies that are less vulnerable to the specific choice of the model, are determined by solving worst-case optimization problems. We study utility maximization problems in continuous-time financial markets with uncertainty about the drift and with a constraint on the admissible strategies that prevents a pure bond investment. The drift uncertainty is taken into account by maximizing the worst-case expected utility given that the drift takes values within some uncertainty set. This set is usually motivated by parameter estimations. For a specific choice of uncertainty sets we give an explicit representation of the optimal strategy and prove a minimax theorem. We then show how uncertainty sets can be defined based on filtering techniques and demonstrate that investors need to account for model uncertainty by choosing a robust strategy instead of relying on drift estimations only.