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

TL;DR

This paper introduces a novel stochastic projected gradient method leveraging Malliavin calculus to optimize reinsurance and investment strategies by directly minimizing ruin probability, with proven convergence and demonstrated numerical effectiveness.

Contribution

It presents a new optimization approach combining stochastic gradient methods and Malliavin calculus for static reinsurance and investment strategies.

Findings

Effective minimization of ruin probability achieved

Convergence of the proposed method established

Numerical experiments confirm practical efficiency

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 H\"older continuous gradient. Numerical experiments show the effectiveness of our proposed method.