In this paper, we consider the optimal per-claim reinsurance problem for an insurer who designs a reinsurance contract with multiple reinsurance participants. In contrast to using the value-at-risk as a short-term risk measure, we take the Lundberg exponent in risk theory as a risk measure for the insurer over a long-term horizon because the Lundberg upper bound performs better in measuring the infinite-time ruin probability. To reflect various risk preferences of the reinsurance participants, we adopt a type of combined premium principle in which the expected premium principle, variance premium principle, and exponential premium principle are all special cases. Based on maximization of the insurer's Lundberg exponent, the optimal reinsurance is formulated within a static setting, and we derive optimal multiple reinsurance strategies within a general admissible policies set. In general, these optimal strategies are shown to have non-piecewise linear structures, differing from conventional reinsurance strategies such as quota-share, excess-of-loss, or linear layer reinsurance arrangements. In some special cases, the optimal reinsurance strategies reduce to classical results.

在本文中，我们考虑了设计具有多个再保险参与者的再保险合同的保险公司的最佳每次索赔再保险问题。与使用风险价值作为短期风险度量相比，我们将风险理论中的 Lundberg 指数作为保险公司长期风险的度量，因为 Lundberg 上限在度量无限时表现更好-时间破产概率。为了反映再保险参与者的不同风险偏好，我们采用了一种组合保费原则，其中预期保费原则、方差保费原则和指数保费原则都是特例。基于保险公司伦德伯格指数的最大化，最优再保险是在静态设置中制定的，并且我们在一般可接受的政策集中得出最优的多重再保险策略。一般来说，这些最优策略具有非分段线性结构，不同于传统的再保险策略，如配额份额、超额损失或线性分层再保险安排。在某些特殊情况下，最优再保险策略简化为经典结果。