模糊厌恶保险人的稳健最优再保险策略
Robust Optimal Per-loss Reinsurance Strategy for an Ambiguity-Averse Insurer
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摘要: 本文探究了连续时间框架下模糊厌恶保险人在无穷维再保险空间中的均衡再保险策略.假定保险人的盈余过程服从带扰动的Cram\'er-Lundberg(C-L)模型,且盈余全部投入到无风险利率市场.保险人采取均衡再保险策略以最大化带有惩罚的均值方差目标函数,我们通过求解拓展的HJB方程组得到了均衡再保险策略及其相应值函数,其中均衡再保险策略是成数再保险和超额损失再保险的混合形式或者是其对偶形式.最后, 我们探究了保险人的模糊厌恶参数及其他主要参数对其均衡再保险策略和相应值函数的影响.Abstract: We investigate the equilibrium reinsurance strategy in an infinite reinsurance space for an ambiguity-averse insurer (AAI) under a continuous-time framework. We assume that the surplus process of the AAI follows the Cram\'er-Lundberg (C-L) model perturbed by standard Brownian motion, and the insurer invests his surplus in a risk-free asset. We present the equilibrium reinsurance strategy and its corresponding value function by solving extended Hamilton-Jacobi-Bellman (HJB) system equations, and we find that the AAI's equilibrium reinsurance strategy to maximize the time-inconsistent penalty-dependent mean-variance reward function is a combination of quota-share with excess of loss reinsurance or its dual form. Detailed numerical analyses are presented to illustrate the various effects of insurer aversion to various uncertainties and other parameters on the equilibrium reinsurance strategy and its corresponding value function.