CEV模型下鲁棒最优投资和超额损失再保险问题研究

Research on Robust Optimal Investment and Excess-of-Loss Reinsurance under CEV Model

摘要: 本文研究了一个模糊厌恶保险公司的最优投资和超额损失再保险策略问题。金融市场包含一个无风险资产和一个有风险资产，其中有风险的资产价格服从CEV模型，保险公司可以购买超额损失再保险，并将其盈余投资到金融市场中，且保险公司的盈余过程近似为带漂移的布朗运动。这篇文章的目标是最大化最小最终财富的指数效用函数的期望。通过使用动态规划方法，我们解决了HJB方程并且得到了最优策略以及值函数的表达式。最后，我们用数值例子来说明模型参数对最优策略的影响。

Abstract: In this paper, we investigate an optimal investment and excess-of-loss reinsurance strategy for an ambiguity-averse insurer (AAI). The financial market consists of one risk-free asset and one risky asset whose price is modeled by a constant elasticity of variance (CEV) model. The insurer can purchase excess-of-loss reinsurance and invest in the financial market. The surplus process of the insurer is approximated by a Brownian motion with drift. The objective is to maximize the minimal expected exponential utility function of the insurer's terminal wealth. By using the dynamic programming approach, we solve the Hamilton-Jacobi-Bellman (HJB) equation and derive the closed form expression of the optimal strategy and the corresponding value function for exponential utility function. Finally, we present numerical examples to illustrate the effects of model parameters on the optimal investment and reinsurance strategies.