线性红利边界下带干扰的风险模型的破产理论

Ruin Theory of a Perturbed Risk Model with Linear Dividend Barrier

针对保险公司的运营会受利率等不确定性因素的影响的问题,本文建立了具有线性分红策略的带干扰的的经典风险模型。利用全概率公式、泰勒展开式及积分变换法,得到了罚金折现函数、破产概率及生存概率满足的积分-微分方程.当红利策略为常值红利策略时,得到了罚金折现函数满足的更新方程,并借助算子变换及相应的复合几何分布,推导出了罚金折现函数的解析表达式.这些量对于保险公司设计相应的财务预警系统或保险监督部门设计某些监督指标系统等问题具有参考价值或指导作用.

The operation of insurance companies will be affected by interest rates or other uncertain factors. In this study, a classical risk model perturbed by diffusion with a linear dividend barrier was established. By using the formula of full probability, the Taylor expansion and the method of integral transform, the integro-differential equations for the Gerber-Shiu functions, ruin probability and survival probability were derived. A renewal equation for the Gerber-Shiu function was obtained in the presence of a constant dividend barrier. The explicit expressions of the Gerber-Shiu function were derived by employing Laplace transforms and some compound geometric distribution functions. These results will provide guidance for insurance companies to design corresponding financial early warning systems or for insurance supervision departments to design monitoring index systems.