保险红利的最优棘轮效应
Optimal ratcheting of dividends in insurance
摘要：
我们解决了风险理论中一个长期存在的开放问题，即如果股息率永远不会降低，从保险盈余过程中支付股息的最优策略。这里的最优性准则是最大化破产时刻的总折现股息支付的期望值。在经典的Cramér-Lundberg风险模型框架下，我们求解了相应的二维最优控制问题，并证明了该值函数是相应的哈密顿-雅可比-贝尔曼方程的唯一粘性解.我们还表明，价值函数可以任意接近棘轮策略，只有有限数量的可能的股息率和确定的自由边界和最佳策略，在几个具体的例子。这些实现表明，与经典的无约束最优股息策略相比，棘轮限制不会导致大的效率损失。
英文摘要：
We address a long-standing open problem in risk theory, namely the optimal strategy to pay out dividends from an insurance surplus process, if the dividend rate can never be decreased. The optimality criterion here is to maximize the expected value of the aggregate discounted dividend payments up to the time of ruin. In the framework of the classical Cramér-Lundberg risk model, we solve the corresponding two-dimensional optimal control problem and show that the value function is the unique viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. We also show that the value function can be approximated arbitrarily closely by ratcheting strategies with only a finite number of possible dividend rates and identify the free boundary and the optimal strategies in several concrete examples. These implementations illustrate that the restriction of ratcheting does not lead to a large efficiency loss when compared to the classical un-constrained optimal dividend strategy.
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