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Truncated stop loss as optimal reinsurance agreement in one-period models. (English) Zbl 1156.62363
Summary: We consider several one-period reinsurance models and derive a rule which minimizes the ruin probability of the cedent for a fixed reinsurance risk premium. The premium is calculated according to the economic principle, generalized zero-utility principle, Esscher principle or mean-variance principle. It turns out that a truncated stop loss is an optimal treaty in the class of all reinsurance contracts. The result is also valid for models not involving ruin probability. An example is the Arrow model with the Kahneman-Tversky value function.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
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[1] DOI: 10.1111/j.0022-4367.2004.00097.x · doi:10.1111/j.0022-4367.2004.00097.x
[2] An Introduction to Mathematical Risk Theory (1979) · Zbl 0431.62066
[3] DOI: 10.1214/aoap/1060202834 · Zbl 1046.62113 · doi:10.1214/aoap/1060202834
[4] ASTIN Bulletin 33 pp 57– (2003) · Zbl 1098.91551 · doi:10.2143/AST.33.1.1039
[5] Insurance: Mathematics and Economics 25 pp 387– (1999)
[6] DOI: 10.1108/eb043451 · doi:10.1108/eb043451
[7] Insurance: Mathematics and Economics 33 pp 381– (2003)
[8] DOI: 10.1017/S0515036100004773 · doi:10.1017/S0515036100004773
[9] DOI: 10.1007/s007800200073 · Zbl 1066.91052 · doi:10.1007/s007800200073
[10] DOI: 10.1017/S0515036100006619 · doi:10.1017/S0515036100006619
[11] DOI: 10.1214/aoap/1031863173 · Zbl 1021.60061 · doi:10.1214/aoap/1031863173
[12] Ruin probabilities (2000)
[13] Scandinavian Actuarial Journal 2 pp 55– (2001)
[14] DOI: 10.1007/s007800050075 · Zbl 0958.91026 · doi:10.1007/s007800050075
[15] Scandinavian Actuarial Journal 3 pp 189– (2004)
[16] American Economic Review 53 pp 941– (1963)
[17] DOI: 10.1002/pamm.200310305 · Zbl 1354.91076 · doi:10.1002/pamm.200310305
[18] Encyclopedia of Actuarial Science (2004) · Zbl 1114.62112
[19] Stochastic Processes for Insurance and Finance (1999) · Zbl 0940.60005
[20] DOI: 10.2143/AST.19.2.2014906 · doi:10.2143/AST.19.2.2014906
[21] DOI: 10.1017/S0515036100006322 · doi:10.1017/S0515036100006322
[22] Insurance: Mathematics and Economics 35 pp 527– (2004)
[23] Scandinavian Actuarial Journal 1 pp 28– (2004)
[24] DOI: 10.1017/S0515036100013866 · doi:10.1017/S0515036100013866
[25] DOI: 10.2307/1914185 · Zbl 0411.90012 · doi:10.2307/1914185
[26] Insurance: Mathematics and Economics 35 pp 21– (2004)
[27] DOI: 10.1007/PL00000042 · Zbl 1049.93090 · doi:10.1007/PL00000042
[28] DOI: 10.1111/1467-9965.00066 · Zbl 0999.91052 · doi:10.1111/1467-9965.00066
[29] Scandinavian Actuarial Journal 1 pp 166– (1998)
[30] DOI: 10.1017/S051503610001343X · doi:10.1017/S051503610001343X
[31] DOI: 10.1007/s007800200095 · Zbl 1069.91051 · doi:10.1007/s007800200095
[32] Stochastic Control with Application in Insurance 1856 (2004)
[33] Aspects of Risk Theory (1991) · Zbl 0717.62100
[34] A unified approach to generate risk measures (2003) · Zbl 1098.91539
[35] Insurance Premiums (1984)
[36] North American Actuarial Journal 8 pp 1– (2004)
[37] Encyclopedia of Actuarial Science (2004) · Zbl 1114.62112
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