论文标题
动态最佳再保险和股息付款在有限的时间范围内
Dynamic optimal reinsurance and dividend-payout in finite time horizon
论文作者
论文摘要
本文研究了在有限的时间范围内的保险公司的动态最佳再保险和股息付款问题。该公司的目标是最大化预期的累计折扣股息支出，直到更早的破产或成熟度为止。允许该公司在整个时间范围内动态购买再保险合同，以减少其与其他再保险公司的风险敞口。这是一个混合的奇异经典控制问题，相应的汉密尔顿 - 雅各比 - 贝尔曼方程是具有完全非线性操作员并受到梯度约束的变异不等式。我们通过惩罚近似方法获得了值函数的$ c^{2,1} $平滑度，并获得其梯度函数的比较原理，以便可以建立有效的数值方案来计算值函数。我们发现，剩余时间空间可以通过风险稳定性和时间依赖性的再保险屏障和时间依赖于时间依赖的股息 - 付款屏障将盈余空间分为三个非重叠区域。随着盈余的增加，保险公司应面临更高的风险；一旦其盈余向上越过再保险障碍，就会面临整个风险；并支付超过股息支付障碍的所有储量。还提供了这些区域的估计地区。
This paper studies a dynamic optimal reinsurance and dividend-payout problem for an insurance company in a finite time horizon. The goal of the company is to maximize the expected cumulative discounted dividend payouts until bankruptcy or maturity which comes earlier. The company is allowed to buy reinsurance contracts dynamically over the whole time horizon to cede its risk exposure with other reinsurance companies. This is a mixed singular-classical control problem and the corresponding Hamilton-Jacobi-Bellman equation is a variational inequality with a fully nonlinear operator and subject to a gradient constraint. We obtain the $C^{2,1}$ smoothness of the value function and a comparison principle for its gradient function by the penalty approximation method so that one can establish an efficient numerical scheme to compute the value function. We find that the surplus-time space can be divided into three non-overlapping regions by a risk-magnitude and time-dependent reinsurance barrier and a time-dependent dividend-payout barrier. The insurance company should be exposed to a higher risk as its surplus increases; be exposed to the entire risk once its surplus upward crosses the reinsurance barrier; and pay out all its reserves exceeding the dividend-payout barrier. The estimated localities of these regions are also provided.
