Accelerated Portfolio Optimization with Conditional Value-at-Risk Constraints using a Cutting-Plane Method

TL;DR

This paper introduces a cutting-plane method for efficiently solving large-scale portfolio optimization problems with CVaR constraints, reducing computational resources compared to traditional reformulation techniques.

Contribution

It proposes a novel cutting-plane algorithm to solve CVaR-constrained portfolio optimization directly, avoiding the large variable increase of existing reformulation methods.

Findings

Significant reduction in computational resources needed.

Efficiently solves large CVaR portfolio problems.

Applicable to reinsurance portfolio optimization.

Abstract

Financial portfolios are often optimized for maximum profit while subject to a constraint formulated in terms of the Conditional Value-at-Risk (CVaR). This amounts to solving a linear problem. However, in its original formulation this linear problem has a very large number of linear constraints, too many to be enforced in practice. In the literature this is addressed by a reformulation of the problem using so-called dummy variables. This reduces the large number of constraints in the original linear problem at the cost of increasing the number of variables. In the context of reinsurance portfolio optimization we observe that the increase in variable count can lead to situations where solving the reformulated problem takes a long time. Therefore we suggest a different approach. We solve the original linear problem with cutting-plane method: The proposed algorithm starts with the solution of a relaxed problem and then iteratively adds cuts until the solution is approximated within a preset threshold. This is a new approach. For a reinsurance case study we show that a significant reduction of necessary computer resources can be achieved.