SIAM Journal on Control and Optimization, Volume 58, Issue 4, Page 1822-1845, January 2020.
We address a long-standing open problem in risk theory, namely finding the optimal strategy to pay out dividends from an insurance surplus process if the dividends are paid according to a dividend rate that is not allowed to decrease. 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 unconstrained optimal dividend strategy.

中文翻译：

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保险股利的最优棘轮

SIAM控制与优化杂志，第58卷，第4期，第1822-1845页，2020年1月。
我们解决了风险理论中一个长期存在的开放性问题，即找到一种最佳策略，即如果按照不允许降低的股息率支付股息，则可以从保险盈余过程中支付股息。此处的最优标准是使折现股息支付总额的期望值最大化，直到破产为止。在经典的Cramér-Lundberg风险模型的框架中，我们解决了相应的二维最优控制问题，并证明了价值函数是相应的Hamilton-Jacobi-Bellman方程的唯一粘性解。我们还表明，可以通过采用有限数量的可能股息率的棘轮策略来任意近似地近似值函数，并在几个具体示例中确定自由边界和最优策略。这些实现说明，与经典的无约束最优分红策略相比，棘轮的限制不会导致较大的效率损失。