Kluppelberg and Stadtmuller (1998) proved a precise asymptotic formula for the ruin probability of the classical interest force and regularly varying tailed claims when the initial capital u tends to infinity . This paper extends their results in several aspects as follows: First, the risk models are the Conditional Poisson and Non-Qici Poisson Process respectively; Second, the ruin probability is replaced by the finite time ruin probability within time T and the claimsize is of Subexponential family which is more wide then that of regularly varying's family. At last, the diffusion term of Brownian Motion is considered. construct et ψ(u;T) be the finite time ruin probability in the renewal risk model, where u is the initial capital of the company and $T$ denotes some given time bound. Under the assumption that the distribution of the claim size belongs to the Extended regular variation class, this paper obtains an asymptotic formula for ψ(u;T). This result improves the related works in the recent literature.
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机译：Kluppelberg和Stadtmuller（1998）证明了一种精确的渐近公式，用于古典利益力的破坏概率，并且当初始资本U倾向于无穷大时，定期不同的拖尾索赔。本文在几个方面延伸了它们的结果，如下所示：首先，风险模型分别是条件泊松和非奇基泊松过程;其次，毁灭概率被时间t的有限时间破坏概率所取代，并且据称强化是子统计家庭，这更广泛地是定期不同的家庭。最后，考虑了布朗运动的扩散项。构造等（U; t）是续订风险模型中有限的时间毁灭概率，其中您是公司的初始资本，$ T $表示一些给定的时间绑定。在假设索赔大小的分布属于扩展常规变化类别的情况下，本文获得了ψ（U; T）的渐近式。这一结果在最近的文献中提高了相关工程。
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