论文标题
与重新保险相关的多个业务保险，对股息策略的随机优化优化
Stochastic optimization of the Dividend strategy with reinsurance in correlated multiple insurance lines of business
论文作者
论文摘要
本文解决了一家在多个业务保险业务下运营的保险公司，涉及最佳动态再保险政策和动态股息策略的随机控制问题。风险过程采用了具有稀疏依赖性结构的总索赔模型。在优化方法中，相对于股息和再保险策略的累积预期折扣股息支出的最大值被视为价值函数。该值函数的特征是相关的Hamilton-Jacobi-Bellman（HJB）方程的最小超级粘度解。已将有限差异方法（FDM）用于值函数的数值解决方案和最佳控制策略，并提供了该数值解决方案与价值函数的收敛证明。本文的发现为保险公司提供了见解，以便基于他们运营的线路，他们可以选择最佳动态再保险策略的向量，因此可以将其一部分风险转移到几个再保险公司。
The present paper addresses the issue of the stochastic control of the optimal dynamic reinsurance policy and dynamic dividend strategy, which are state-dependent, for an insurance company that operates under multiple insurance lines of business. The aggregate claims model with a thinning-dependence structure is adopted for the risk process. In the optimization method, the maximum of the cumulative expected discounted dividend payouts with respect to the dividend and reinsurance strategies are considered as value function. This value function is characterized as the smallest super Viscosity solution of the associated Hamilton-Jacobi- Bellman (HJB) equation. The finite difference method (FDM) has been utilized for the numerical solution of the value function and the optimal control strategy and the proof for the convergence of this numerical solution to the value function is provided. The findings of this paper provide insights for the insurance companies as such that based upon the lines in which they are operating, they can choose a vector of the optimal dynamic reinsurance strategies and consequently transfer some part of their risks to several reinsurers.
