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Expected present value of total dividends in a delayed claims risk model under stochastic interest rates. (English) Zbl 1231.91460
Summary: A compound binomial risk model with a constant dividend barrier under stochastic interest rates 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. In the evaluation of the expected present value of dividends, the interest rates are assumed to follow a Markov chain with finite state space. 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.
MSC:
91G30Interest rates (stochastic models)
91B30Risk theory, insurance
References:
[1]Bara, K.; Hwa-Sung, K.; Jeongsim, K.: A risk model with paying dividends and random environment, Insurance: mathematics and economics 42, 717-726 (2008) · Zbl 1152.91589 · doi:10.1016/j.insmatheco.2007.08.001
[2]Claramunt, M. M.; Mármol, 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 2, 149-159 (2003)
[3]De Finetti, B., 1957. Su un’ impostazione alternativa dell teoria collettiva del rischio. In: Transactions of the XVth International Congress of Actuaries, 2, pp. 433–443
[4]Dickson, D. C. M.; Waters, H. R.: Some optimal dividends problems, ASTIN bulletin 34, 49-74 (2004) · Zbl 1097.91040 · doi:10.2143/AST.34.1.504954
[5]Frosting, E.: On the expected time to ruin and the expected dividends when dividends are paid while the surplus is above a constant barrier, Journal of applied probability 42, 595-607 (2005) · Zbl 1116.91054 · doi:10.1239/jap/1127322014
[6]Gerber, H. U.; Shiu, E. S. W.: Optimal dividends: analysis with Brownian motion, North American actuarial journal 8, 1-20 (2004) · Zbl 1085.62122
[7]Landriault, D.: On a generalization of the expected discounted penalty function in a discrete-time insurance risk model, Applied stochastic models in business and industry 24, 525-539 (2008) · Zbl 1199.91084 · doi:10.1002/asmb.713
[8]Li, S.: The moments of the present value of total dividends under stochastic interest rates, Australian actuarial journal 14, No. 2, 175-192 (2008)
[9]Li, S.: On a class of discrete time renewal risk models, Scandinavian actuarial journal 4, 241-260 (2005) · Zbl 1142.91043 · doi:10.1080/03461230510009745
[10]Li, S.; Garrido, J.: On a class of renewal risk models with a constant dividend barrier, Insurance: mathematics and economics 35, 691-701 (2004) · Zbl 1122.91345 · doi:10.1016/j.insmatheco.2004.08.004
[11]Waters, H. R.; Papatriandafylou, A.: Ruin probabilities allowing for delay in claims settlement, Insurance: mathematics and economics 4, 113-122 (1985) · Zbl 0565.62091 · doi:10.1016/0167-6687(85)90005-8
[12]Wu, X., Li, S., 2006. On a discrete time risk model with delayed claims and a constant dividend barrier. Working paper, http://repository.unimelb.edu.au/10187/579
[13]Xiao, Y. T.; Guo, J. Y.: The compound binomial risk model with time-correlated claims, Insurance: mathematics and economics 41, 124-133 (2007) · Zbl 1119.91059 · doi:10.1016/j.insmatheco.2006.10.009
[14]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 3, 319-326 (2008)
[15]Yuen, K. C.; Guo, J. Y.: Ruin probabilities for time-correlated claims in the compound binomial model, Insurance: mathematics and economics 29, 47-57 (2001) · Zbl 1074.91032 · doi:10.1016/S0167-6687(01)00071-3
[16]Yuen, K. C.; Guo, J. Y.; Ng, K. W.: On ultimate ruin in a delayed-claims risk model, Journal of applied probability 42, 163-174 (2005) · Zbl 1074.60089 · doi:10.1239/jap/1110381378
[17]Zhou, X.: On a classical risk model with a constant dicidend barrier, North American actuarial journal 9, 95-108 (2005) · Zbl 1215.60051 · doi:http://www.soa.org/news-and-publications/publications/journals/naaj/naaj-oct-2005.aspx