论文标题
二维风险模型的最佳股息以及两个分支机构的毁灭
Optimal dividends for a two-dimensional risk model with simultaneous ruin of both branches
论文作者
论文摘要
我们认为，在一个分支的盈余可能会变成负面的假设下，所谓的退化双变量风险模型中的最佳股息问题。更具体地说，我们解决了最大化折扣股息的随机控制问题，直到同时毁灭了保险公司的两个分支机构，这表明最佳价值功能满足了某个汉密尔顿 - 雅各布利 - 贝尔曼（HJB）方程。此外，我们证明最佳值函数是所述HJB方程的最小粘度解，满足某些生长条件。在一些其他假设下，我们表明最佳策略在于所有可允许策略的某个子类范围内，并将二维控制问题减少到一维控制问题。结果通过数值示例和蒙特卡洛模拟值函数来说明。
We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing discounted dividends until simultaneous ruin of both branches of an insurance company by showing that the optimal value function satisfies a certain Hamilton-Jacobi-Bellman (HJB) equation. Further, we prove that the optimal value function is the smallest viscosity solution of said HJB equation, satisfying certain growth conditions. Under some additional assumptions, we show that the optimal strategy lies within a certain subclass of all admissible strategies and reduce the two-dimensional control problem to a one-dimensional one. The results are illustrated by a numerical example and Monte-Carlo simulated value functions.
