A Decomposition of the Ruin Probability for Risk Process with Vasicek Interest Rate  

作　　者：徐林 汪荣明 姚定俊 

机构地区：[1]School of Mathematics and Computer Science, Anhui Normal University, Wuhu, 241000 [2]School of Fianance and Statistics, East China Normal University, Shanghai, 200241

出　　处：《Northeastern Mathematical Journal》2008年第1期45-53,共9页东北数学（英文版）

基　　金：The NNSF(10671072,10726075)of China;the Doctoral Program Foundation(20060269016)of the Ministry of Education of China;the National Basic Research Program(973 Program,2007CB814904)of China.

摘　　要：In this paper, it is assumed that an insurer with a jump-diffusion risk process would invest its surplus in a bond market, and the interest structure of the bond market is assumed to follow the Vasicek interest model. This paper focuses on the studying of the ruin problems in the above compounded process. In this compounded risk model, ruin may be caused by a claim or oscillation. We decompose the ruin probability for the compounded risk process into two probabilities： the probability that ruin caused by a claim and the probability that ruin caused by oscillation. Integro-differential equations for these ruin probabilities are derived. When the claim sizes are exponentially distributed, the above-mentioned integro-differential equations can be reduced into a three-order partial differential equation.In this paper, it is assumed that an insurer with a jump-diffusion risk process would invest its surplus in a bond market, and the interest structure of the bond market is assumed to follow the Vasicek interest model. This paper focuses on the studying of the ruin problems in the above compounded process. In this compounded risk model, ruin may be caused by a claim or oscillation. We decompose the ruin probability for the compounded risk process into two probabilities： the probability that ruin caused by a claim and the probability that ruin caused by oscillation. Integro-differential equations for these ruin probabilities are derived. When the claim sizes are exponentially distributed, the above-mentioned integro-differential equations can be reduced into a three-order partial differential equation.

关 键 词：integro-differential equation jump-diffusion process ruin probability Vasicek model 

分 类 号：O211[理学—概率论与数理统计]