Sample Average Approximation for Portfolio Optimization under CVaR constraint in an (re)insurance context

TL;DR

This paper proves the convergence and discusses the effectiveness of the Sample Average Approximation method for solving portfolio optimization problems with CVaR constraints in (re)insurance, providing practical tools for risk management.

Contribution

It establishes convergence, convergence rate, and solution uniqueness for SAA applied to CVaR-constrained portfolio optimization, under mild assumptions.

Findings

SAA converges for CVaR-constrained optimization problems

A convergence rate is provided for the SAA method

Results support practical application in (re)insurance risk management

Abstract

We consider optimal allocation problems with Conditional Value-At-Risk (CVaR) constraint. We prove, under very mild assumptions, the convergence of the Sample Average Approximation method (SAA) applied to this problem, and we also exhibit a convergence rate and discuss the uniqueness of the solution. These results give (re)insurers a practical solution to portfolio optimization under market regulatory constraints, i.e. a certain level of risk.