带利息的风险模型中破产前索赔次数的矩

Study on joint distribution of time to ruin and number of claims until ruin in classical risk model with interest

在带利息的经典风险模型中,计算了公司初始盈余u=0时Gerber-Shiu型函数φ_(r,δ)(0)以及在第n次索赔时破产的概率p_n(0).得出了公司初始盈余u> 0时第n次索赔时破产的概率p_n(u)的表达式,利用这个公式及拉普拉斯变换得出了u=0及u> 0时破产前索赔次数的矩.

In the classic risk model with interest,the Gerber-Shiu-type functionφr,δ(0)and the probability of ruin p n(0)at the time of the n th claim were calculated.The expression of probability of ruin p n(u)for the n th claim at the time of initial surplus u >0 of the company was obtained.By using this formula and Laplace transform,the moments of the number of claims before bankruptcy at u=0 and u >0 were obtained.