Multi-objective risk-averse two-stage stochastic programming problems

TL;DR

This paper introduces a novel convex vector optimization approach for multi-objective risk-averse two-stage stochastic programming, utilizing an extended Benson's algorithm and scenario-wise decomposition to efficiently solve complex portfolio optimization problems.

Contribution

It develops a new convex vector optimization formulation with set-valued constraints and extends Benson's algorithm, including duality-based decomposition methods for risk-averse stochastic problems.

Findings

Effective solution algorithms for multi-objective risk-averse stochastic problems

Successful application to multi-asset portfolio optimization with transaction costs

Demonstrated computational efficiency and solution quality

Abstract

We consider a multi-objective risk-averse two-stage stochastic programming problem with a multivariate convex risk measure. We suggest a convex vector optimization formulation with set-valued constraints and propose an extended version of Benson's algorithm to solve this problem. Using Lagrangian duality, we develop scenario-wise decomposition methods to solve the two scalarization problems appearing in Benson's algorithm. Then, we propose a procedure to recover the primal solutions of these scalarization problems from the solutions of their Lagrangian dual problems. Finally, we test our algorithms on a multi-asset portfolio optimization problem under transaction costs.