Acta mathematica scientia, Series B >
ON THE RENEWAL RISK MODEL WITH INTEREST AND DIVIDEND
Received date: 2007-10-19
Revised date: 2009-04-11
Online published: 2010-09-20
Supported by
Supported by NSFC (10926161).
We consider that the reserve of an insurance company follows a renewal risk process with interest and dividend. For this risk process, we derive integral equations and exact infinite series expressions for the Gerber-Shiu discounted penalty function. Then we give lower and upper bounds for the ruin probability. Finally, we present exact expressions for the ruin probability in a special case of renewal risk processes.
FANG Ying , WU Rong . ON THE RENEWAL RISK MODEL WITH INTEREST AND DIVIDEND[J]. Acta mathematica scientia, Series B, 2010 , 30(5) : 1730 -1738 . DOI: 10.1016/S0252-9602(10)60166-X
[1] Asmussen S. Ruin Probabilities. Singapore: World Scientific, 2000
[2] Cai J, Dickson D C M. On the expected discounted penalty function at ruin of a surplus process with interest. Insurance: Mathematics and Economics, 2002, 30(3): 389--404
[3] Cai J, Dickson D C M. Upper bounds for ultimate ruin probabilities in the Sparre Andersen model with interest. Insurance: Mathematics and Economics, 2003, 32(1): 61--71
[4] Dickson D C M, Hipp, C. On the time to ruin for Erlang(2) risk process. Insurance: Mathematics and Economics, 2001, 29(3): 333--344
[5] Gerber H U, Shiu E S W. On the time value of ruin. North American Actuarial Journal, 1998, 2(1): 48--78
[6] Gerber H U, Shiu E S W. The time value of ruin in a Sparre Andersen model. North American Actuarial Journal, 2005, 9(2): 49--69
[7] Landriault D, Willmot G. On the Gerber-Shiu discounted penalty function in the Sparre Andersen model with an arbitrary interclaim time distribution. Insurance: Mathematics and Economics, 2008, 42(2): 600--608
[8] Li S, Garrido J. On a class of renewal risk models with a constant dividend barrier. Insurance: Mathematics and Economics, 2004, 35(3): 691--701
[9] Li S, Garrido J. On ruin for the Erlang$(n)$ risk process. Insurance: Mathematics and Economics, 2004, 34(3): 391--408
[10] Li S, Garrido J. On a general class of renewal risk process: analysis of the Gerber-Shiu function. Advances in Applied Probability, 2005, 37: 836--856
[11] Wu R, Wang G, Zhang C. On a joint distribution for the risk process with constant interest rate. Insurance: Mathematics and Economics, 2005, 36(3): 365--374
[12] Willmot G. On the discounted penalty function in the renewal risk model with general interclaim times. Insurance: Mathematics and Economics, 2007, 41(1): 17--31
[13] Yuen K, Wang G, Wu R. On the renewal risk process with stochastic interest. Stochastic Processes and Their Applications, 2006, 116: 1496--1510
/
| 〈 |
|
〉 |