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

doi:10.1016/S0252-9602(13)60111-3

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (6): 1639-1651.doi: 10.1016/S0252-9602(13)60111-3

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

周杰明¹|莫晓云^1,2|欧辉¹|杨向群^1*

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, Changsha 410081, China；
2. Department of Mathematics, Hunan University of Finance and Economics, Changsha 410205, China

收稿日期:2012-05-18 修回日期:2013-01-06 出版日期:2013-11-20 发布日期:2013-11-20
通讯作者: 杨向群，xqyang@hunnu.edu.cn E-mail:zhjm04101@126.com; moxyun72@163.com; bthuiou@sina.com; xqyang@hunnu.edu.cn
基金资助:
This is supported by the NSFC (11171101), Doctoral Fund of Education Ministry of China (20104306110001), the Graduate Research and Innovation Fund of Hunan Province (CX2011B197).

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

ZHOU Jie-Ming¹, MO Xiao-Yun^1,2, OU Hui, YANG Xiang-Qun^1*

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, Changsha 410081, China；
2. Department of Mathematics, Hunan University of Finance and Economics, Changsha 410205, China

Received:2012-05-18 Revised:2013-01-06 Online:2013-11-20 Published:2013-11-20
Contact: YANG Xiang-Qun，xqyang@hunnu.edu.cn E-mail:zhjm04101@126.com; moxyun72@163.com; bthuiou@sina.com; xqyang@hunnu.edu.cn
Supported by:
This is 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/Abstract

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 K_n 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

Abstract:

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 K_n 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.

Key words: compound binomial model, main claim, by-claim, dividend, random income

中图分类号:

60J27

周杰明, 莫晓云, 欧辉, 杨向群. EXPECTED PRESENT VALUE OF TOTAL DIVIDENDS IN THE COMPOUND BINOMIAL MODEL WITH DELAYED CLAIMS AND RANDOM INCOME[J]. 数学物理学报(英文版), 2013, 33(6): 1639-1651.

ZHOU Jie-Ming, MO Xiao-Yun, OU Hui, YANG Xiang-Qun. EXPECTED PRESENT VALUE OF TOTAL DIVIDENDS IN THE COMPOUND BINOMIAL MODEL WITH DELAYED CLAIMS AND RANDOM INCOME[J]. Acta mathematica scientia,Series B, 2013, 33(6): 1639-1651.

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

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

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