论文标题
在离散时间的动态再保险最小化保险公司的资本成本
Dynamic Reinsurance in Discrete Time Minimizing the Insurer's Cost of Capital
论文作者
论文摘要
在经典的静态最佳再保险问题中，保险公司风险敞口的资本成本由货币风险措施确定的风险敞口最小化，这是通过增加Lipschitz保留损失功能的一系列再保险条约。在本文中，我们考虑了在离散时间内这种再保险问题的动态扩展，可以将其视为对风险敏感的马尔可夫决策过程。该模型允许保险索赔和保费收入是随机的，并以一般风险措施和保费原则运作。我们得出了钟声方程，并显示了马尔可夫最佳再保险政策的存在。在无限的计划范围内，该模型被证明是一定程度的，最佳的再保险政策是固定的。结果以明确确定最佳策略的示例进行了说明。
In the classical static optimal reinsurance problem, the cost of capital for the insurer's risk exposure determined by a monetary risk measure is minimized over the class of reinsurance treaties represented by increasing Lipschitz retained loss functions. In this paper, we consider a dynamic extension of this reinsurance problem in discrete time which can be viewed as a risk-sensitive Markov Decision Process. The model allows for both insurance claims and premium income to be stochastic and operates with general risk measures and premium principles. We derive the Bellman equation and show the existence of a Markovian optimal reinsurance policy. Under an infinite planning horizon, the model is shown to be contractive and the optimal reinsurance policy to be stationary. The results are illustrated with examples where the optimal policy can be determined explicitly.
