EUROPT 2024
Abstract Submission

172. Robust multi-objective stochastic control

Invited abstract in session TD-4: Multiobjective Optimization III, stream Multiobjective optimization.

Thursday, 14:10 - 15:50
Room: M:M

Authors (first author is the speaker)

1. Gabriela Kovacova
Department of Mathematics, University of California, Los Angeles
2. Igor Cialenco
Illinois Institute of Technology

Abstract

Model uncertainty is relevant for various dynamic optimization problems. As one example, let us mention the portfolio selection problem -- an investor does not know the true distribution of asset return on the market. Various approaches to handling uncertain stochastic control problems have been developed, among them the robust approach with the aim of optimizing under the worst-case scenario.

While model uncertainty and robust optimization are relatively well understood for standard control problems with a single (scalar) objective, this is much less the case for problems with multiple objectives. In recent years, several (dynamic) problems of financial mathematics have been approached through methods of multi-objective and set optimization. Set-valued Bellman's principle, a version of the well known Bellman's principle for problems with multiple or set-valued objectives, has been derived across different problems.

In this work we explore the robust approach to model uncertainty for multi-objective stochastic control problems. Robust multi-objective optimization has been explored in the static but not in the dynamic setting. We are particularly interested in the application of dynamic programming and the impact model uncertainty has on the set-valued Bellman's principle. We show how the set-valued Bellman's principle is replace by certain set relations (or inclusions) under robustness and present assumptions under which equality can be obtained.

Keywords

Status: accepted

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