A local asymptotic behavior for ruin probability in the renewal risk model

Let be the renewal risk model, with F _X(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 F _X(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. Biography: MING Ruixing (1975–), male, Ph.D. candidate, research direction: insurance mathematics, large deviations and its application.