EXPECTED PRESENT VALUE OF TOTAL DIVIDENDS IN THE COMPOUND BINOMIAL MODEL WITH DELAYED CLAIMS AND RANDOM INCOME  

作　　者：周杰明 莫晓云 欧辉 杨向群 

机构地区：[1]College of Mathematics and Computer Science,Key Laboratory of High Performance Computing and Stochastic Information Processing Ministry of Education of China,Hunan Normal University [2]Department of Mathematics,Hunan University of Finance and Economics

出　　处：《Acta Mathematica Scientia》2013年第6期1639-1651,共13页数学物理学报（B辑英文版）

基　　金：supported by the NSFC(11171101);Doctoral Fund of Education Ministry of China(20104306110001);the Graduate Research and Innovation Fund of Hunan Province(CX2011B197)

摘　　要：In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer＇s arrivals and payments. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are Kn distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer＇s arrivals and payments. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are Kn distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.

关 键 词：compound binomial model main claim by-claim DIVIDEND random income 

分 类 号：O211.6[理学—概率论与数理统计]