Optimal reinsurance and investment via stochastic projected gradient method based on Malliavin calculus

ArXiv ID: 2411.05417 “View on arXiv”

Authors: Unknown

Abstract

This paper proposes a new approach using the stochastic projected gradient method and Malliavin calculus for optimal reinsurance and investment strategies. Unlike traditional methodologies, we aim to optimize static investment and reinsurance strategies by directly minimizing the ruin probability. Furthermore, we provide a convergence analysis of the stochastic projected gradient method for general constrained optimization problems whose objective function has Hölder continuous gradient. Numerical experiments show the effectiveness of our proposed method.

Keywords: Stochastic Projected Gradient Method, Malliavin Calculus, Optimal Reinvestment, Ruin Probability, Constrained Optimization, Insurance and Investment Portfolios

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced mathematics including Malliavin calculus and stochastic optimal control theory, while the empirical section is described in a general sense without specific code, backtest metrics, or implementation details.

  flowchart TD
    A["Research Goal:<br>Minimize Ruin Probability<br>via Optimal Reinsurance & Investment"] --> B["Methodology:<br>Stochastic Projected Gradient Method<br>w/ Malliavin Calculus"]
    B --> C["Inputs:<br>Market Data & Insurance Risk Parameters"]
    C --> D["Computation:<br>Constrained Optimization<br>Hölder Continuous Gradient Analysis"]
    D --> E["Numerical Experiments<br>on Investment Portfolios"]
    E --> F["Key Outcomes:<br>1. Convergent SPGM Algorithm<br>2. Static Optimal Strategies<br>3. Reduced Ruin Probability"]