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

ArXiv ID: 2410.10239 “View on arXiv”

Authors: Unknown

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.

Keywords: Conditional Value-At-Risk, CVaR, Sample Average Approximation, portfolio optimization, risk management, Portfolio Management

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper is mathematically dense, featuring proofs of convergence (SAA), rates, and uniqueness theorems using convex analysis and probability theory. While it discusses the practical context of (re)insurance and portfolio optimization, it lacks any reported backtesting, numerical experiments, or dataset usage, focusing instead on theoretical guarantees.

  flowchart TD
    A["Research Goal: Portfolio Optimization<br>with CVaR Constraints"] --> B{"Methodology: Sample Average Approximation SAA"}
    B --> C["Input: Historical Portfolio Data<br>Scenarios & Parameters"]
    C --> D["Computational Process:<br>Minimize CVaR subject to Constraints"]
    D --> E["Computational Process:<br>Convergence Analysis & Rate Estimation"]
    E --> F["Key Finding 1:<br>Proof of SAA Convergence"]
    F --> G["Key Finding 2:<br>Uniqueness of Solution"]
    G --> H["Outcome: Practical Framework for<br>Reinsurers & Risk Management"]