【作者】 于慧敏；

【导师】 房莹；

【作者基本信息】 山东师范大学 ， 统计学， 2021， 硕士

【摘要】 在保险实践中,再保险合同双方通常对损失分布有不同的看法,因此异质性信念影响着最优再保险策略.基于此,本文以最大化保险人最终财富的期望效用为目标函数研究了异质性信念下的最优再保险问题.为了减少事后道德风险,我们遵循Huberman等人^[26]的观点,假设再保险合同满足赔偿原则和激励相容约束.在扭曲保费原则下,我们得到以下结论:首先,建立了关于异质性信念下最优解的充分必要条件,发现最优解的边际赔偿应为1或0;其次,通过研究不保险和全保险的最优性,解释了保险人选择分出尾部风险和不分出尾部风险的现象;再次,对于任意次优再保险合同,都提出了一种切实可行的改进方案;最后,给出了止损再保险最优的充分条件,并且在止损最优的情况下明确得出了最优免赔额水平,发现当保险人的风险厌恶程度降低时,优先选择较高的免赔额。更多还原

【Abstract】 In the insurance practice,both parties in reinsurance contract have heterogeneous beliefs in the loss distribution,so heterogeneous beliefs affect the optimal reinsurance strategy.On this basis,this thesis studies an optimal reinsurance problem under heterogeneous belief,and takes maximizing the expected utility of the insurer’s final wealth as the objective function.In order to reduce ex post moral hazard,we follow the viewpoint of Huberman et al^[26]and assume that the reinsurance contract follows the principle of indemnity and incentive compatibility constraint.We obtain the following conclusions under the distortion premium principle:firstly,we derive a necessary and sufficient condition for the optimal solution under heterogeneous beliefs,and find that the marginal indemnity of an optimal solution should be either 1 or 0;moreover,by studying the optimality of no insurance and full insurance,we explain the phenomenon that the insurer choose to cede tail risk and not to cede tail risk;in addition,we develop a practical scheme to enhance any suboptimal reinsurance contract;finally,we also give the sufficient condition that the stop-loss reinsurance is the optimal solution,and clearly deduce the optimal retention level when the stop-loss reinsurance is optimal,we find that when the risk aversion of the insurer decreases,the deductible level increases.更多还原