模糊厌恶下含相关索赔的最优投资再保险问题

Optimal Reinsurance and Investment Problem with Correlated Claims under Ambiguity Aversion

本文考虑了当保险公司在考虑相关索赔的基础上以破产概率最小化为目标时的最优投资及再保险问题。假设保险公司是模糊厌恶的,并且被允许购买比例再保险来分散部分风险以及投资一种风险资产来实现公司的盈余保值,其中风险资产的价格过程符合几何布朗运动。由此得到了Hamilton-Jacobi-Bellman方程,并在此基础上通过对方程的求解得到了保险公司的最优投资和再保险策略及值函数的表达式。最后本文给出了数值例子用以描述不同模型参数对保险公司的最优策略的影响。

This paper considers the optimal investment and reinsurance problem when an insurance company aims to minimize the probability of ruin while considering correlated claims. It is assumed that the insurer is ambiguity aversion and allowed to purchase proportional reinsurance to spread some risk and invest a risk asset is used to realize the company’s surplus preservation, and the price process of the risk asset follows the geometric Brownian motion. From this, the Hamilton-Jacobi- Bellman equation is obtained, and on this basis, the optimal investment and reinsurance strategy and the expression of value function of the insurance company is obtained by solving the equation. Finally, numerical examples are given to describe the trend of the insurance company’s optimal strategy on the basis of different model parameters.