最小化破产概率的保险人鲁棒投资再保险策略研究

王雨薇; 荣喜民

最小化破产概率的保险人鲁棒投资再保险策略研究

引用本文：王雨薇，荣喜民.最小化破产概率的保险人鲁棒投资再保险策略研究[J].经济数学,2020,(4):1-10

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作者	单位
王雨薇，荣喜民	（天津大学数学学院，天津 300350）

中文摘要:在模型不确定条件下，研究以破产概率最小化为目标的模糊厌恶型保险公司的最优投资再保险问题. 假设保险公司可投资于一种风险资产，也可购买比例再保险. 分别考虑风险资产的价格过程服从随机波动率模型和非随机波动率模型的两种情况，根据动态规划原理建立相应的HJB方程，得到保险公司的最优鲁棒投资再保险策略和价值函数的解析解. 最后，通过数值模拟分析了各模型参数对最优策略和价值函数的影响.

中文关键词:破产概率模型不确定随机波动率投资策略再保险 HJB方程随机最优控制

Optimal Reinsurance and Investment Strategies for Insurers with Ambiguity Aversion: Minimizing the Probability of Ruin

Abstract:This paper considers a robust optimal investment and reinsurance problem for an ambiguity averse insurer (AAI) who aims to minimize the probability of ruin. The insurer is allowed to purchase proportional reinsurance and to invest in a risky asset. We consider two cases in which the price process of risky assets follows stochastic volatility model and non stochastic volatility model respectively. According to the dynamic programming principle, we derive the corresponding Hamilton-Jacobi-Bellman (HJB) equation, and obtain the optimal strategy and value function explicitly. Finally, we illustrate the effects of model parameters on optimal strategy and value function by numerical analysis.

keywords:probability of ruin model ambiguity stochastic volatility investment strategy reinsurance HJB equation stochastic optimal control

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