【摘要】 在考虑模型的不确定性因素下,研究了两家相互竞争保险公司的随机微分投资与再保险博弈问题。假设金融市场中包含两种资产:一种为无风险资产,另一种为风险资产。两家保险公司一方面通过购买比例再保险来控制风险,另一方面通过将其盈余投资到金融市场中以实现财富的保值增值。以最大化最坏情形下终端财富相对差值绩效的期望效用为目标,构建了一个两家保险公司之间的鲁棒非零和随机微分博弈模型。运用随机动态规划方法导出了Hamilton-Jacobi-Bellman(HJB)方程,通过求解HJB方程得到了鲁棒最优投资与再保险策略的解析表达。最后通过数值算例分析了模型的参数变动对鲁棒最优投资与再保险策略的影响。更多还原

【Abstract】 This paper investigates a non-zero-sum stochastic differential game between two competitive insurers, who are concerned about the potential model ambiguity and aim to seek the robust optimal investment and reinsurance strategies. The ambiguity-averse insurers are allowed to purchase proportional reinsurance to mitigate individual claim risks; and can invest in a financial market consisting of one risk-free asset and one risky asset. The objective of each insurer is to maximize the expected utility of his terminal surplus relative to that of his competitor under the worst-case scenario of the alternative measures. Applying the techniques of stochastic dynamic programming, we derive the robust Nash equilibrium investment and reinsurance strategies explicitly. Finally,some numerical examples are conducted to illustrate the influence of model parameters on the equilibrium investment and reinsurance strategies and draw some economic interpretations from these results.更多还原