We consider a perturbed compound Poisson risk model with randomized dividend-decision times. Different from the classical barrier dividend strategy, the insurance company makes decision on whether or not paying off dividends at some discrete time points (called dividend-decision times). Assume that at each dividend-decision time, if the surplus is larger than a barrier b>0, the excess value will be paid off as dividends. Under such a dividend strategy, we study how to compute the moments of the total discounted dividend payments paid off before ruin.
. [J]. Frontiers of Mathematics in China, 2017, 12(2): 493-513.
Zhimin ZHANG,Chaolin LIU. Moments of discounted dividend payments in a risk model with randomized dividend-decision times. Front. Math. China, 2017, 12(2): 493-513.
Albrecher H, Cheung E C K, Thonhauser S. Randomized observation periods for the compound Poisson risk model: Dividends. Astin Bull, 2011, 41(2): 645–672
2
Albrecher H, Claramunt M M, M′armol M. On the distribution of dividend payments in a Sparre Andersen model with generalized Erlang(n) interclaim times. Insurance Math Econom, 2005, 37(2): 324–334
https://doi.org/10.1016/j.insmatheco.2005.05.004
3
Avanzi B, Cheung E C K, Wong B, Woo J K. On a periodic dividend barrier strategy in the dual model with continuous monitoring of solvency. Insurance Math Econom, 2013, 52(1): 98–113
https://doi.org/10.1016/j.insmatheco.2012.10.008
4
Choi M C H, Cheung E C K. On the expected discounted dividends in the Cram′er-Lundberg risk model with more frequent ruin monitoring than dividend decisions. Insurance Math Econom, 2014, 59: 121–132
https://doi.org/10.1016/j.insmatheco.2014.08.009
5
De Finetti B. Su un impostazione alternativa della teoria collectiva del rischio. Transactions of the XVth International Congress of Actuaries, 1957, 2: 433–443
6
Gerber H U. An extension of the renewal equation and its application in the collective theory of risk. Scand Actuar J, 1970, 1970(3-4): 205–210
https://doi.org/10.1080/03461238.1970.10405664
Kyprianou A E. Introductory Lectures on Fluctuations of L′evy Processes with Applications. Berlin: Springer-Verlag, 2006
9
Li S. The distribution of the dividend payments in the compound poisson risk model perturbed by diffusion. Scand Actuar J, 2006, 2006(2): 73–85
https://doi.org/10.1080/03461230600589237
Lin X S, Willmot G E, Drekic S. The classical risk model with a constant dividend barrier: Analysis of the Gerber-Shiu discounted penalty function. Insurance Math Econom, 2003, 33(3): 551–566
https://doi.org/10.1016/j.insmatheco.2003.08.004
13
Tsai C C L. On the discounted distribution functions of the surplus process perturbed by diffusion. Insurance Math Econom, 2001, 28(3): 401–419
https://doi.org/10.1016/S0167-6687(01)00067-1
14
Tsai C C L. On the expectations of the present values of the time of ruin perturbed by diffusion. Insurance Math Econom, 2003, 32(3): 413–429
https://doi.org/10.1016/S0167-6687(03)00130-6
15
Tsai C C L, Willmot G E. A generalized defective renewal equation for the surplus process perturbed by diffusion. Insurance Math Econom, 2002, 30(1): 51–66
https://doi.org/10.1016/S0167-6687(01)00096-8
16
Yin C, Wen Y. Optimal dividend problem with a terminal value for spectrally positive L′evy processes. Insurance Math Econom, 2013, 53(3): 769–773
https://doi.org/10.1016/j.insmatheco.2013.09.019
17
Yin C, Wen Y, Zhao Y. On the optimal dividend problem for a spectrally positive L′evy process. Astin Bull, 2014, 44(3): 635–651
https://doi.org/10.1017/asb.2014.12
Zhang Z, Cheung E C K. The Markov additive risk process under an Erlangized dividend barrier strategy. Methodol Comput Appl Probab, 2016, 18(2): 275–306
https://doi.org/10.1007/s11009-014-9414-7
