ISBN 9783843942546

978-3-8439-4254-6, Reihe Mathematik

Dorothee Westphal
Model Uncertainty and Expert Opinions in Continuous-Time Financial Markets

189 Seiten, Dissertation Technische Universität Kaiserslautern (2019), Hardcover, A5

Zusammenfassung / Abstract

Model uncertainty is a challenge inherent in many applications of mathematical models. Optimization procedures in general take place under a particular model which might be misspecified due to statistical estimation errors and incomplete information. Difficulties arise since a strategy which is optimal under the approximating model might perform rather badly in the true model.

We consider utility maximization problems in continuous-time financial markets. It is well known that drift parameters in such markets are difficult to estimate. To obtain strategies that are robust with respect to a misspecification of the drift we consider a worst-case utility maximization problem with ellipsoidal uncertainty sets and a constraint that prevents a pure bond investment. By a dual approach we derive an explicit representation of the optimal strategy and prove a minimax theorem. This enables us to show that the optimal strategy converges to a generalized uniform diversification strategy as uncertainty increases.

To come up with a reasonable uncertainty set, investors can use filtering techniques to estimate the drift based on return observations as well as external sources of information, so-called expert opinions. In a financial market with Gaussian drift we investigate the asymptotic behavior of the filter as the frequency of expert opinions tends to infinity. We show that the information obtained from observing the expert opinions is asymptotically the same as that from observing a certain diffusion process which we interpret as a continuous-time expert.

Our observations about how expert opinions improve drift estimates can be used for our robust utility maximization problem. We show that our duality approach carries over to a financial market with non-constant drift. A time-dependent uncertainty set can then be defined based on a filter. We apply this to various investor filtrations and investigate which effect expert opinions have on the robust strategies.