The Asymptotic of Finite Time Ruin Probabilitiesfor Risk Model with Variable Interest Rates
Yu Jinyou,Hu Yijun,Wei Xiao
Guanghua School of Management, Peking University,School of Mathematics and Statistics, Wuhan University,School of Insurance and CIAS, Central Universityof Finance and Economics
Abstract��Consider a discrete time risk model \[ U_n=(U_{n-1}+Y_n)(1+r_n)-X_n,\qq n=1,2,\cdots, \] where $U_0=x>0$ is the initial reserve of an insurance company, $r_n$ the interest rates, $Y_n$ the total amount of premiums, $X_n$ the total amount of claims and $U_n$ the reserve at time $n$. Under some mild conditions on $Y_n$ and $r_n$, we obtain the uniform asymptotics relation for the finite time ruin probabilities $\psi(x,N)\sim\tsm_{k=1}^{N}\ol{F}_X((1+r_1)\cdots(1+r_n)x)$ as $x\to\infty$, where $\psi(x,N)=\pr\big(\min\limits_{0\leq n\leq N}U_n<0$ $|U_0=x\big)$, $N\geq1$, $\ol{F}_X(x)$ is the tail distribution of $X_1$, and the uniformity is with respect to $N\geq1$.} \newcommand{\fundinfo}{Supported by the National Natural Science Foundation of China (10671149, 10801139) and Key Project of Philosophy and Social Sciences Research of the Ministry of Education (07JZD0010).
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Yu Jinyou,Hu Yijun,Wei Xiao. The Asymptotic of Finite Time Ruin Probabilitiesfor Risk Model with Variable Interest Rates. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2010, 26(1): 57-65.
