🤖 AI Summary
This paper addresses the optimal asset allocation problem for (re)insurers subject to regulatory Conditional Value-at-Risk (CVaR) constraints. To overcome the computational intractability of exact CVaR-constrained optimization, we propose a sample-average approximation (SAA)-based stochastic optimization framework. First, we establish the strong consistency of the SAA estimator under minimal distributional assumptions, derive an explicit convergence rate, and provide sufficient conditions for uniqueness of the optimal solution. The framework thus bridges theoretical rigor with computational tractability, yielding a provably convergent and implementable risk-compliant investment strategy. It enhances capital efficiency and portfolio robustness while ensuring regulatory compliance and prudent 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.