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Optimal risk control for the excess of loss reinsurance policies. (English) Zbl 1230.91079
Summary: The primary objective of the paper is to explore using reinsurance as a risk management tool for an insurance company. We consider an insurance company whose surplus can be modeled by a Brownian motion with drift and that the surplus can be invested in a risky or riskless asset. Under the above Black-Scholes type framework and using the objective of minimizing the ruin probability of the insurer, we formally establish that the excess-of-loss reinsurance treaty is optimal among the class of plausible reinsurance treaties. We also obtain the optimal level of retention as well as provide an explicit expression of the minimal probability of ruin.

MSC:
91B30 Risk theory, insurance (MSC2010)
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[1] DOI: 10.1007/s001860050001 · Zbl 0947.91043 · doi:10.1007/s001860050001
[2] DOI: 10.1007/s007800200073 · Zbl 1066.91052 · doi:10.1007/s007800200073
[3] DOI: 10.1214/aoap/1031863173 · Zbl 1021.60061 · doi:10.1214/aoap/1031863173
[4] Scandinavian Actuarial Journal 1 pp 55– (2001)
[5] DOI: 10.1080/10920277.2005.10596229 · doi:10.1080/10920277.2005.10596229
[6] DOI: 10.1016/0167-6687(94)00016-6 · Zbl 0814.62068 · doi:10.1016/0167-6687(94)00016-6
[7] Stochastics 77 pp 455– (2005) · Zbl 1058.60002
[8] Introduction to stochastic calculus with applications (1998)
[9] DOI: 10.1016/j.insmatheco.2004.04.004 · Zbl 1052.62107 · doi:10.1016/j.insmatheco.2004.04.004
[10] DOI: 10.1002/asmb.637 · Zbl 1152.91039 · doi:10.1002/asmb.637
[11] Schweizerische Aktuarvereinigung. Mitteilungen 1 pp 15– (2006)
[12] DOI: 10.1088/1469-7688/4/3/007 · doi:10.1088/1469-7688/4/3/007
[13] Aspects of risk theory (1991) · Zbl 0717.62100
[14] Controlled Markov Processes and viscosity solutions (1993) · Zbl 0773.60070
[15] DOI: 10.1088/1469-7688/1/6/301 · doi:10.1088/1469-7688/1/6/301
[16] DOI: 10.1016/j.insmatheco.2004.12.001 · Zbl 1125.91062 · doi:10.1016/j.insmatheco.2004.12.001
[17] DOI: 10.1287/moor.20.4.937 · Zbl 0846.90012 · doi:10.1287/moor.20.4.937
[18] DOI: 10.1007/s007800050075 · Zbl 0958.91026 · doi:10.1007/s007800050075
[19] DOI: 10.1016/S0167-6687(96)00017-0 · Zbl 1065.91529 · doi:10.1016/S0167-6687(96)00017-0
[20] Schweizerische Aktuarvereinigung. Mitteilungen 2 pp 173– (2004)
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