论文标题
以外币为莱维保险风险模型支付的最佳股息
Optimal Dividends Paid in a Foreign Currency for a Lévy Insurance Risk Model
论文作者
论文摘要
本文考虑了以外币支付股息的保险公司的最佳股息分配问题。在没有股息支付的情况下，我们的风险过程遵循频谱负面的莱维过程。我们假设汇率是通过指数级的流程来描述的，可能包含所考虑的保险公司盈余等相同风险来源。控制机制选择了股息支付的量。目的是最大化预期的股息支付，直到毁灭时期和毁灭时的罚款，这是毁灭性不足的规模越来越多的功能。完整的解决方案显示给相应的随机控制问题。通过相应的汉密尔顿 - 雅各比 - 贝尔曼方程，我们找到了最佳的必要条件，以实现单个股息屏障策略。许多数值示例说明了理论分析。
This paper considers an optimal dividend distribution problem for an insurance company where the dividends are paid in a foreign currency. In the absence of dividend payments, our risk process follows a spectrally negative Lévy process. We assume that the exchange rate is described by a an exponentially Lévy process, possibly containing the same risk sources like the surplus of the insurance company under consideration. The control mechanism chooses the amount of dividend payments. The objective is to maximise the expected dividend payments received until the time of ruin and a penalty payment at the time of ruin, which is an increasing function of the size of the shortfall at ruin. A complete solution is presented to the corresponding stochastic control problem. Via the corresponding Hamilton--Jacobi--Bellman equation we find the necessary and sufficient conditions for optimality of a single dividend barrier strategy. A number of numerical examples illustrate the theoretical analysis.
