2020/09/30 by Jörn Saß, Jörn Sass, Dorothee Westphal
Decision Sciences · Economics, Econometrics and Finance · Engineering · Mathematics · #Computer science #Economics #Finance #Financial market #Mathematical economics #Mathematical optimization #Mathematics #Maximization #Microeconomics #Minimax #Optimal control #Optimization problem #Portfolio #Portfolio optimization #Profit (economics) #Profit maximization #Reservoir Engineering and Simulation Methods #Risk and Portfolio Optimization #Robust optimization #Set (abstract data type) #Stochastic control #Stochastic optimization #Stochastic processes and financial applications #Stochastic programming #Utility maximization #Utility maximization problem #msc:91B16 #msc:91G10 #msc:93E20 #q-fin.PM
paper · pdf · doi:10.1142/s0219024921500205
published as International Journal of Theoretical and Applied Finance 24 (4), 2021 · 26 pages, 1 figure
arxiv created 2021/05/30 · openalex publication_date 2021/06/01 · openalex created_date 2021/06/22 · arxiv updated 2021/11/04 · openalex updated_date 2026/07/28
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.