In this paper, we examine how a monopolistic reinsurer designs a Bowley reinsurance contract, under the assumption that the reinsurer will default on payment if the compensated loss exceeds the sum of the initial capital and the premium charged from the contract. The problem is divided into two subproblems faced by the insurer and the reinsurer in turn. The optimal reinsurance contract is analyzed when both the insurer and the reinsurer minimize their retained risks, as quantified by the VaR measure, and the optimal ceded loss function and the optimal pricing function are provided. Explicit expressions are then derived when the reinsurer adopts either VaR- or TVaR-based regulation capital and charges premiums by the expected-value premium principle. Numerical examples using exponential and Pareto distributions are provided to illustrate the sensitivity effect generated by the confidence levels of the VaR for both parties, as well as those for the initial capitals on the set of Bowley reinsurance contracts.

在本文中，我们研究了垄断再保险公司如何设计鲍利再保险合同，假设如果补偿损失超过初始资本和合同中收取的保费之和，再保险公司将拖欠付款。该问题分为保险公司和再保险公司依次面临的两个子问题。当保险公司和再保险公司都将其保留风险最小化（通过 VaR 度量量化）时，将分析最优再保险合同，并提供最优分出损失函数和最优定价函数。当再保险公司采用基于VaR或基于TVaR的监管资本并按照期望值保费原则收取保费时，就会得到明确的表达式。提供了使用指数分布和帕累托分布的数值示例来说明双方的 VaR 置信水平以及鲍利再保险合同集的初始资本的置信水平所产生的敏感性效应。