ABSTRACT

This paper investigates a non-zero-sum stochastic differential game between two competitive CARA insurers, where we adopt the different classes of premium principles (including the expected value premium principle, the variance premium principle and the exponential premium principle) and each insurer aims to maximize the expected exponential utility of his terminal wealth relative to that of his competitor. Moreover, both insurers are allowed to purchase reinsurance treaty to mitigate individual claim risks and can invest in a financial market consisting of a risk-free asset, a risky asset where the instantaneous rate of investment return follows an Ornstein-Uhlenbeck process which can reflect the changes of bull market and bear market. The optimal reinsurance strategy has a non-trivial structure which is distinguished from the conventional proportional and excess-of-loss reinsurance strategies. Furthermore, we derive the optimal reinsurance and investment strategies under the variance premium principle and expected value principle. In addition, we give another model which considers the correlation between risk model and financial market under the expected value principle. Finally, numerical analyses are provided to analyze the effects of model parameters on the optimal strategies under different cases.

摘要

本文研究了两家竞争性 CARA 保险公司之间的非零和随机微分博弈，我们采用不同类别的保费原则（包括期望值保费原则、方差保费原则和指数保费原则），每家保险公司的目标是最大化他的终端财富相对于他的竞争对手的预期指数效用。此外，两家保险公司都被允许购买再保险协议以降低个人索赔风险，并可以投资于由无风险资产组成的金融市场，这是一种投资回报率遵循 Ornstein-Uhlenbeck 过程的风险资产，该过程可以反映牛市和熊市的变化。最优再保险策略具有不同于传统比例和超额损失再保险策略的非平凡结构。此外，我们在方差溢价原则和期望值原则下得出了最优的再保险和投资策略。此外，我们给出了另一个模型，该模型在期望值原则下考虑了风险模型与金融市场的相关性。最后通过数值分析分析模型参数对不同情况下最优策略的影响。我们给出了另一种在期望值原则下考虑风险模型与金融市场相关性的模型。最后通过数值分析分析模型参数对不同情况下最优策略的影响。我们给出了另一种在期望值原则下考虑风险模型与金融市场相关性的模型。最后通过数值分析分析模型参数对不同情况下最优策略的影响。