具有分红、流动储备金和利率的风险模型的绝对破产

摘要

建立了阈值分红策略下具有流动储备金、投资利率和贷款利率的复合泊松风险模型。利用全概率公式和泰勒展式，推导出了该模型的Gerber‐Shiu函数和绝对破产时刻的累积分红现值期望满足的积分‐微分方程及边界条件，借助Volterra方程，给出了Gerber‐Shiu函数的解析表达式。%This paper studied the compound Poisson risk model with liquid reserves ,credit interest and debit interest in the presence of a threshold dividend strategy .By the total law of probability and Taylor's expansion ,we first obtained the inte‐gro‐differential equations with boundary conditions satisfying the Gerber‐Shiu function and presented the closed form expres‐sions for the Gerber‐Shiu function .Secondly ,we derived the integro‐differential equations with boundary conditions satisfying the expected discounted present value of all dividends until absolute ruin by employing Volterra equations .