ROBUST UTILITY MAXIMIZATION IN A MULTIVARIATE FINANCIAL MARKET WITH STOCHASTIC DRIFT

Jörn Sass () and Dorothee Westphal
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Jörn Sass: Department of Mathematics, Technische Universität Kaiserslautern, P. O. Box 3049, 67653 Kaiserslautern, Germany
Dorothee Westphal: Department of Mathematics, Technische Universität Kaiserslautern, P. O. Box 3049, 67653 Kaiserslautern, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2021, vol. 24, issue 04, 1-28

Abstract: We study a utility maximization problem in a financial market with a stochastic drift process, combining a worst-case approach with filtering techniques. Drift processes are difficult to estimate from asset prices, and at the same time optimal strategies in portfolio optimization problems depend crucially on the drift. We approach this problem by setting up a worst-case optimization problem with a time-dependent uncertainty set for the drift. Investors assume that the worst possible drift process with values in the uncertainty set will occur. This leads to local optimization problems, and the resulting optimal strategy needs to be updated continuously in time. We prove a minimax theorem for the local optimization problems and derive the optimal strategy. Further, we show how an ellipsoidal uncertainty set can be defined based on filtering techniques and demonstrate that investors need to choose a robust strategy to be able to profit from additional information.

Keywords: Portfolio optimization; drift uncertainty; robust strategies; stochastic filtering; minimax theorems (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024921500205

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