×

zbMATH — the first resource for mathematics

The compound binomial model with randomized decisions on paying dividends. (English) Zbl 1147.91349
Summary: Consider a discrete time risk process based on the compound binomial model. The insurer pays a dividend of 1 with a probability \(q_{0}\) when the surplus is greater than or equal to a non-negative integer \(x\). We derive recursion formulas and an asymptotic estimate for the ruin probability, the probability function of the surplus prior to the ruin time, and the severity of ruin, etc.

MSC:
91B30 Risk theory, insurance (MSC2010)
60K05 Renewal theory
60K10 Applications of renewal theory (reliability, demand theory, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Cai, J., Ruin probabilities and penalty functions with stochastic rates of interest, Stochastic processes and their applications, 112, 53-78, (2004) · Zbl 1070.60043
[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, 30, 389-404, (2002) · Zbl 1074.91027
[3] Chen, J.; Chen, X., Special matrices, (2001), Tsinghua Beijing, pp. 129-131 (in Chinese)
[4] Cheng, S.; Gerber, H.U.; Shiu, E.S.W., Discounted probabilities and ruin theory in the compound binomial model, Insurance: mathematics and economics, 26, 239-250, (2000) · Zbl 1013.91063
[5] Cheng, S.; Zhu, R., The asymptotic formulas and lundberg upper bound in fully discrete risk model, Applied mathematics. A journal of Chinese universities series A, 16, 3, 348-358, (2001), (in Chinese) · Zbl 0992.91052
[6] DeVylder, F.E., Advanced risk theory: A self-contained introduction, (1996), Editions de l’Universite de Bruxelles Brussels
[7] DeVylder, F.E.; Marceau, E., Classical numerical ruin probabilities, Scandinavian actuarial journal, 2, 1, 191-207, (1996)
[8] Dickson, D.C.M., Some comments on the compound binomial model, Astin bulletin, 24, 33-45, (1994)
[9] Gerber, H.U., Mathematical fun with the compound binomial process, Astin bulletin, 18, 161-168, (1988)
[10] Gerber, H.U.; Cheng, S.; Yan, Y., An introduction to mathematical risk theory, (1997), WPC Beijing, (in Chinese)
[11] Gerber, H.U.; Shiu, E.S.W., The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin, Insurance: mathematics and economics, 21, 129-137, (1997) · Zbl 0894.90047
[12] Grandell, J., Aspects of risk theory, (1993), Springer Beijing, p. 2
[13] Karlin, S.; Taylor, H.M., A first course in stochastic processes, (1975), Academic Press New York, pp. 81-89
[14] Pullman, N.J., Matrix theory and its applications, (1976), Marcel Dekker, Inc. New York, pp. 213-214 · Zbl 0339.15001
[15] Shiu, E.S.W., The probability of eventual ruin in the compound binomial model, Astin bulletin, 19, 179-190, (1989)
[16] Willmot, G.E., Ruin probabilities in the compound binomial model, Insurance: mathematics and economics, 12, 133-142, (1993) · Zbl 0778.62099
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.