具有分红、流动储备金和利率的风险模型的绝对破产

A Risk Model with Credit and Debit Interests,Liquid Reserves and Dividends Under Absolute Ruin

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 integro-differential equations with boundary conditions satisfying the Gerber-Shiu function and presented the closed form expressions 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.