The Asymptotic of Finite Time Ruin Probabilities for Risk Model with Variable Interest Rates
Yu Jinyou1,2 Hu Yijun2 Wei Xiao3(1Guanghua School of Management,Peking University,Beijing,100871)(2School of Mathematics and Statistics,Wuhan University,Hubei,430072)(3School of Insurance and CIAS,Central University of Finance and Economics,Beijing,100081)
Consider a discrete time risk model Un=Un1+Yn)(1+rn)Xn,n=1,2,…,where U0=x0 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 probabilities ψ(x,N)～sum from k=1 to N(FX((1+r1)…(1+rn)x)) as x→∞,where ψ(x,N)=P min 0≤n≤N Un0U0=x,N≥1,FX(x) is the tail distribution of X1,and the uniformity is with respect to N≥1.


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