THE JOINT DISTRIBUTIONS OF SOME ACTUARIAL DIAGNOSTICS FOR THE JUMP-DIFFUSION RISK PROCESS  

作　　者：吕玉华 吴荣 徐润 

机构地区：[1]Department of Mathematics, Qufu Normal University [2]School of Mathematics Sciences and LPMC, Nankai University

出　　处：《Acta Mathematica Scientia》2010年第3期664-676,共13页数学物理学报（B辑英文版）

基　　金：Supported by the National Natural Sci-ence Foundations of China (10271062 and 10471119);the Natural Science Foundation of Shandong Province(Y2004A06, Y2008A12, and ZR2009AL015);the Science Foundations of Shandong Provincial Education Department (J07yh05);the Science Foundations of Qufu Normal University (XJ0713, Bsqd200517)

摘　　要：In this article, the joint distributions of several actuarial diagnostics which are important to insurers＇ running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus process leaving zero ultimately （simply, the ultimately leaving-time）, the surplus immediately prior to ruin, the supreme profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. The explicit expressions for their distributions are obtained mainly by the various properties of Levy process, such as the homogeneous strong Markov property and the spatial homogeneity property etc, moveover, the many properties for Brownian motion.In this article, the joint distributions of several actuarial diagnostics which are important to insurers＇ running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus process leaving zero ultimately （simply, the ultimately leaving-time）, the surplus immediately prior to ruin, the supreme profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. The explicit expressions for their distributions are obtained mainly by the various properties of Levy process, such as the homogeneous strong Markov property and the spatial homogeneity property etc, moveover, the many properties for Brownian motion.

关 键 词：Jump-diffusion risk process Brownian motion time of ruin ultimately leaving-time homogeneous strong Markov property 

分 类 号：O211.67[理学—概率论与数理统计]