标题： 基于Malliavin微积分的随机投影梯度法最优再保险与投资 显示英文标题

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

摘要： 本文提出了一种新的方法，使用随机投影梯度法和马尔可夫微积分来获得最优再保险和投资策略。 与传统方法不同，我们旨在通过直接最小化破产概率来优化静态投资和再保险策略。 此外，我们提供了随机投影梯度法在目标函数具有霍尔德连续梯度的一般约束优化问题中的收敛性分析。 数值实验展示了我们所提出方法的有效性。 显示英文摘要

摘要： 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.