一类特殊双险种风险模型的Gerber-Shiu函数

Gerber-Shiu function of a special risk model with double-type insurance

研究了一类常利率下可能发生两类索赔的双复合泊松风险模型,其中保费及保费收取时间随机。利用全期望公式和累进均值法则,得到了Gerber-Shiu函数所满足的积分方程,并由所得到的积分方程推出了破产概率、破产时Laplace变换、破产时赤字和破产前瞬间盈余的期望折现等精算量的积分方程。

In this paper,a double compound Poisson risk model is studied,on the condition of a constant interest rate,random premium,random arrival time of premium and two kinds of claims may occur.Under such a model,the integral equation for the Gerber-Shiu function is obtained by the law of total expectation and progressive mean rule.The integral equations for the ruin probability,the Laplace transform of the time of ruin,the expected discounted value of the deficit at ruin and the surplus immediately before ruin,and other actuarial diagnostics are derived from the integral equation.