Kluppelberg and Stadtmuller (1998, Scand. Actuar. J.,no. 1,49-58) 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 0(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 0(u; T). This result improves the related works in the recent literature.
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