中文摘要：

这篇文章，研究了带投资和债务利率的SparreAndersenJK险模型的绝对破产问题．首先，得到了在绝对破产时折扣罚金函数满足的带边界值的积分一微分方程．然后，得到了绝对破产时折扣罚金函数满足的更新方程，进而分别在索赔额是轻尾和重尾时，得到了折扣罚金函数两个的渐进结果．最后，在索赔间隔服从广义Erlang（2）分布和索赔额服从指数分布的情况下，得到了具体的表达式和一些数值结果．

英文摘要：

In this paper, we study absolute ruin problems for the Sparre Andersen risk process with generalized Erlang（n）-distributed inter-claim times, investment and debit interest. We first give a system of integro-differential equations with certain boundary conditions satisfied by the expected discounted penalty function at absolute ruin. Second, we obtain a defective renewal equation under some special cases, then based on the defective renewal equation we derive two asymptotic results for the expected discounted penalty function when the initial surplus tends to infinity for the light- tailed claims and heavy-tailed claims, respectively. Finally, we investigate some explicit solutions and numerical results for generalized Erlang（2） inter-claim times and exponential claims.