研究在扰动的Sparre Andersen模型中保险公司破产前发生的理赔次数,这里理赔时间间隔服从Erlang(2)分布;l(u;n+1)表示保险公司破产前发生n+1次理赔的概率,h(u;n)表示公司破产是由于振荡引起的且发生在第n次和第n+1次理赔之间的概率.l-(s;n+1),-h(s;n)分别表示l(u;n+1),h(u;n)的拉普拉斯变换(n=1,2,…),得到了-l(s;n+1)和h-(s;n)的递推公式,由此运用Mathematics等数学软件可以算出l(u;n+1)及h(u;n). (2) distribution; l (u; n + 1) represents the probability that an insurance company will make n + 1 claims before the bankruptcy, and the number of claims before the bankruptcy of the insurer in Sparre Andersen model is studied. h (u; n) represents the probability that a company’s bankruptcy is due to oscillations and occurs between the nth and n + 1th claims.1- (s; n + 1), - h The Laplacian of l (u; n + 1), h (u; n) (n = 1,2, ...) ) Recursive formula, thus using Mathematics and other mathematical software can be calculated l (u; n +1) and h (u; n).