A Local Asymptotic Behavior for Ruin Probability in the Renewal Risk Model

摘要

Let R(t)=u+ct-sum from(i=1) to (N(t)) Xi,t≥0 be the renewal risk model,with FX ( x )being the distribution function of the claim amount X. Let ψ (u ) be the ruin probability with initial surplus u. Under the condition of FX (x) ∈ S *(γ ),γ≥ 0,by the geometric sum method,we derive the local asymptotic behavior for ψ (u ,u + z for every 0＜z＜∞. On one hand,the asymptotic behavior of ψ ( u) can be derived from the result obtained. On the other hand,the result of this paper can be applied to the insurance risk management of an insurance company.