变利率风险模型有限时间破产概率的渐近(英文)

The Asymptotic of Finite Time Ruin Probabilities for Risk Model with Variable Interest Rates

本文考虑离散时间风险模型Un=Un-1+Yn)(1+rn)-Xn,n=1,2,…,其中U0=x>0为保险公司的初始准备金,rn为在第n个时刻的利率,Yn为到时刻n为止的总保费收入,Xn为到时刻n为止的所支付的全部索赔,Un表示保险公司在时刻n的盈余.当Yn和rn满足某些温和条件时,我们得到了在x→∞时,有限时间破产概率ψ(x,N)=Pmin0≤n≤NUn<0|U0=x关于N≥1的一致渐近的关系式ψ(x,N)～sum from k=1 to N(FX((1+r1)…(1+rn)x)),其中FX(x)是X1的尾分布.

Consider a discrete time risk model where Un=（Un-1＋Yn）（1＋rn）-Xn,n=1,2,…, U0 = x 〉 0 is the initial reserve of an insurance company, rn the interest rates, Yn the total amount of premiums, Xn the total amount of claims and Un the reserve at time n. Under some mild conditions on Yn and rn, we obtain the uniform asymptotics relation for the finite time ruin N probabilities ψ（x,N）～^N∑ k=1 Fx（（1＋r1）…（1＋rn）x）） as x→∞, where ψ（x,N）=P（min0≤n≤NUn〈0｜U0=x关于N≥1,Fx（x） is the tail distribution of X1, and the uniformity is with respect to N ≥ 1.