Wasserstein Distributionally Robust Optimization with Expected Value Constraints

TL;DR

This paper develops a Wasserstein distributionally robust optimization framework for stochastic programs with expected value constraints, providing reformulations, feasibility criteria, and demonstrating its effectiveness in portfolio optimization with real and simulated data.

Contribution

It introduces a novel DRO approach with decision-dependent ambiguity sets, reformulates the problem into a finite-dimensional, potentially convex form, and offers feasibility criteria for practical implementation.

Findings

Reformulation into finite-dimensional optimization problems

Feasibility criteria based on Wasserstein radius and parameters

Numerical validation in portfolio optimization with real data

Abstract

We investigate a stochastic program with expected value constraints, addressing the problem in a general context through Distributionally Robust Optimization (DRO) approach using Wasserstein distances, where the ambiguity set depends on the decision variable. We demonstrate that this approach can be reformulated into a finite-dimensional optimization problem, which, in certain instances, can be convex. Moreover, we establish criteria for determining the feasibility of the problem concerning the Wasserstein radius and the parameter governing the constraint. Finally, we present numerical results within the context of portfolio optimization. In particular, we highlight the distinctions between our approach and several existing non-robust methods, using both simulated data and real financial market data.