Title: Utility maximization under model uncertainty
Authors: Dorothee Westphal - TU Kaiserslautern (Germany) [presenting]
Joern Sass - University of Kaiserslautern (Germany)
Abstract: When modelling financial markets one is frequently confronted with model uncertainty. This is meant in the sense that parameters of the model, e.g. the drift of a stock, or the distributions of some factors in the model are only known up to a certain degree. Risk-averse investors in such a market try to maximize their worst-case expected utility. This naturally leads to considering robust optimization problems. We investigate optimal trading strategies for a robust utility maximization problem in a continuous-time Black-Scholes type financial market and impose a constraint that prevents a pure bond investment. The optimal strategy of an investor depends on how uncertain the parameters in the market are. As the degree of model uncertainty increases, investors tend to rely on robust strategies. We show that if the uncertainty exceeds a certain threshold simple strategies such as uniform portfolio diversification outperform more sophisticated ones due to being more robust. This generalizes previous results for a discrete-time model to continuous time.