Acta mathematica scientia, Series B >
EXPECTED PRESENT VALUE OF TOTAL DIVIDENDS IN THE COMPOUND BINOMIAL MODEL WITH DELAYED CLAIMS AND RANDOM INCOME
Received date: 2012-05-18
Revised date: 2013-01-06
Online published: 2013-11-20
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).
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.
Key words： compound binomial model; main claim; by-claim; dividend; random income
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 . DOI: 10.1016/S0252-9602(13)60111-3
[1] Waters H R, Papatriandafylou A. Ruin probabilities allowing for delay in claims settlement. Insurance: Mathematics and Economics, 1985, 4: 113–122
[2] Yuen K C, Guo J Y. Ruin probabilities for time-correlated claims in the compound binomial model. Insurance: Mathematics and Economics, 2001, 29: 47–57
[3] Yuen K C, Guo J Y, Ng K W. On ultimate ruin in a delayed-claims risk model. Journal of Applied Probability, 2005, 42: 163–174
[4] Xiao Y T, Guo J Y. The compound binomial risk model with time-correlated claims. Insurance: Mathe-matics and Economics, 2007, 41: 124–133
[5] Xie J H, Zou W. Ruin probabilities of a risk model with time-correlated claims. Journal of the Graduate School of the Chinese Academy of Sciences, 2008, 3: 319–326
[6] De Finetti B. Su un’impostazione alternativa della teoria collettiva del rischio. Transactions of the XVth International Congress of Actuaries, 1957, 2: 433–443
[7] Claramunt M M, Marmol M, Alegre A. A note on the expected present value of dividends with a constant barrier in the discrete time model. Bulletin of the Swiss Association of Actuaries, 2003, 2: 149–159
[8] Gerber H U, Shiu E S W. Optimal dividends:Analysis with Brownian motion. North American Actuarial Journal, 2004, 8: 1–20
[9] Zhou M, Guo J Y. Classical risk model with threshold dividend strategy. Acta Mathematica Scientia, 2008, 28B(2): 355–362
[10] Fang Y, Wu R. On the renewed risk model with interest and dividend. Acta Mathematica Scientia, 2010, 30B(5): 1730–1738
[11] Wu X, Li S. On a discrete time risk model with delayed claims and a constant dividend barrier. Working paper, 2006. http://repository.unimelb.edu.au/10187/579
[12] Bao Z H, Liu H. The compound binomial risk model with delayed claims and random income. Mathematical and Computer Modeling, 2012, 55: 1315–1323
[13] Dong H, Zhao X H, Liu Z M. Risk process with barrier and random income. Applied Mathematics E-Notes, 2010, 10: 191–198
[14] Bao Z H. The expected discounted penalty at ruin in the risk process with random income. Applied Mathematics and Computation, 2006, 179: 559–566
[15] Bao Z H, Ye Z X. The Gerber-Shiu discounted penalty function in the delayed renewal risk process with random income. Applied Mathematics and Computation, 2007, 184: 857–863
[16] Yang H, Zhang Z. On a class of renewal risk model with random income. Applied Stochastic Models in Business and Industry, 2009, 25: 678–695
[17] Li S. On a class of discrete time renewal risk models. Scandinavian Actuarial Journal, 2005, 4: 271–284
/
| 〈 |
|
〉 |