We investigate the optimal reinsurance problems in this paper, specifically, the stop-loss strategies that can bring mutual benefit to both the insurance company and the reinsurance company. The utility improvement constraints are adopted by both contracting parties to guarantee that a reinsurance contract will bring higher expected utilities of wealth to the two participants. We also introduce five risk criteria that reflect the interests of both parties. Under each optimality criterion, we obtain explicit expressions of optimal stop-loss retentions and the corresponding optimised value of objective functions. The upper and lower bounds of expected utility increments under the optimal stop-loss retentions are provided. In the numerical example, we analyse the expected utility improvements under the criterion of minimising total Value-at-Risk. Notable increases in the lower bound of total utility increments are observed after adopting the joint utility improvement constraints.

中文翻译：

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具有共同效用约束的最优止损再保险

我们在本文中研究最优再保险问题，特别是可以使保险公司和再保险公司互惠互利的止损策略。双方采用效用提高约束条件，以确保再保险合同将为两个参与者带来更高的预期财富效用。我们还介绍了反映双方利益的五个风险标准。在每个最优准则下，我们获得最优止损保持率的显式表达式以及目标函数的相应最优值。提供了最佳止损保留条件下预期效用增量的上限和下限。在数值示例中，我们在最小化总风险价值的标准下分析了预期的效用提高。