Abstract
This paper considers the problem of minimizing the VaR and CTE of an insurer’s retained risk by controlling the combinational quota-share and stop-loss reinsurance strategy. With a constrained reinsurance premium, the authors give the explicit reinsurance forms and the minimal VaR and CTE of retained risk in the case of quota-share after stop-loss reinsurance and the case of stop-loss after-quota-share reinsurance respectively. Finally, the authors conclude that the quota-share after stop-loss is a better reinsurance strategy than stop-loss after quota-share to minimize the VaR and CTE with a same constrained reinsurance premium. And the pure stop-loss reinsurance is preferred for an insurer with a high level regulatory requirement.
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References
J. Cai and K. S. Tan, Optimal retention for a stop-loss reinsurance under the VaR and CTE risk measures, ASTIN Bulletin, 2007, 37(1): 93–112.
C. M. Dickson and H. R. Waters, Reinsurance and ruin, Insurance: Mathematics and Economics, 1996, 19: 61–80.
L. Centeno, Excess of loss reinsurance and Gerber’s inequality in the Sparre Anderson model, Insurance Mathematics and Economics, 2002, 31: 415–427.
R. Verlaak and J. Beirlant, Optimal reinsurance programs: An optimal combination of several reinsurance protections on a heterogeneous insurance portfolio, Insurance: Mathematics and Economics, 2003, 33: 381–403.
L. Centeno, On combining quota-share and excess-of-loss, ASTIN Bulletin, 1985, 15(1): 49–63.
J. Cai, K. S. Tan, C. Weng, and Y. Zhang, Optimal reinsurance under the VaR and CTE risk measures, Insurance Mathematics and Economics, 2008, 43(1): 185–196.
N. L. Bowers, H. U. Gerber, J. C. Hickman, et al., Actuarial Mathematics, Society of Actuaries, Itacsa, IL, 1986.
L. Gajek and D. Zagrodny, Insurer’s optimal reinsurance strategies, Insurance: Mathematics and Economics, 2000, 27: 105–112.
L. Gajek and D. Zagrodny, Optimal reinsurance under general risk measure, Insurance: Mathematics and Economics, 2004a, 34: 227–240.
L. Gajek and D. Zagrodny, Reinsurance arrangements maximizing insurer’s survival probability, The Journal of Risk and Insurance, 2004b, 71(3): 421–435.
M. Kaluszka, Optimal reinsurance under mean-variance premium principles, Insurance: Mathematics and Economics, 2001, 28: 61–67.
M. Kaluszka, Truncated stop-loss as reinsurance agrement in one-period models, ASTIN Bulletin, 2005, 35(2): 337–349.
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This research is supported by Supported by the Natural Science Foundation of China under Grant Nos. 10701082 and 70801068, the major program of Key Research Institute of Humanities and Social Sciences at Universities (08JJD790145), and a grant from the “project 211 (Phase III)”.
This paper was recommended for publication by Editor Shouyang WANG.
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Zhou, M., Dong, H. & Xu, J. Optimal combinational of quota-share and stop-loss reinsurance contracts under VaR and CTE with a constrained reinsurance premium. J Syst Sci Complex 24, 156–166 (2011). https://doi.org/10.1007/s11424-011-7127-3
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DOI: https://doi.org/10.1007/s11424-011-7127-3