VaR seviyesi kısıtları altında karı maksimize eden optimal saklama payı

Öz

Farklı riske-maruz-değer (VaR) seviyesi kısıtları altında sigortacının karını maksimize eden optimal saklama payı problemi incelenmiştir. Toplam hasar fazlası reasürans anlaşmalarında optimal saklama payının belirlenmesinde, benzetim optimizasyonu içeren bir paket program kullanımı önerilmektedir. Toplam hasar fazlası reasürans anlaşması altında verilen bir risk seviyesi için elde edilebilecek maksimum kar ve verilen bir ortalama getiri için elde edilebilecek minimum risk seviyesi etkin sınır analizi ile belirlenmiştir.

Anahtar Kelimeler

• Toplam hasar fazlası reasürans,saklama payı,kar maksimizasyonu,beklenen değer prim ilkesi,standart sapma prim ilkesi,riske-maruz-değer (VaR),etkin sınır,benzetim optimizasyonu.

Optimal retention for profit maximizing under VaR levels constraints

Öz

We consider the problem of finding the optimal retention that maximizes the insurer's profit under different value-at-risk level constraints. We propose simulation optimization for the determination of optimal retention in stop-loss reinsurance using a package program which incorporates a simulation optimizer. Efficient frontier analysis is carried out to investigate maximum profit obtainable for a given risk level and minimum risk level obtainable for a given mean return under stop-loss reinsurance.

Anahtar Kelimeler

• Stop-loss reinsurance,retention,profit maximization,expected value premium principle,standard deviation premium principle,value-at-risk (VaR),efficient frontier,simulation optimization.

Kaynakça

1. [1] M. J. Goovaerts, F. De Vylder, J. Haezendonck, Insurance Premiums: Theory and Applications, North Holland, Amsterdam, 1984.
2. [2] V.R. Young, Premium Principles, in: B. Sundt, J. Teugels, J. (Eds), Encyclopedia of Actuarial Science, New York: John Wiley & Sons, Ltd. 2004.
3. [3] K. Borch, An attempt to determine the optimum amount of stop-loss reinsurance, in: Transactions of the 16th International Congress of Actuaries, 1960, pp. 597-610.
4. [4] M. Denuit, C. Vermandele, Optimal reinsurance and stop-loss order, Insurance: Math. Econ. 22 (1998), 229-233.
5. [5] M. Kaluszka, Optimal reinsurance under mean-variance premium principles, Insurance: Math. Econ. 28 (2001), 61-67.
6. [6] M. Taksar, C. Markussen, Optimal dynamic reinsurance policies for large insurance portfolios. Finance and Stoch. 7 (2003), 97-121.
7. [7] L. He, P. Hou, Z. Liang, Optimal control of the insurance company with proportional reinsurance policy under solvency constraints, Insurance: Math. Econ. 43 (2008), 474-479.
8. [8] M.L. Centeno, M. Guerra, The optimal reinsurance strategy - the individual claim case, Insurance: Math. Econ. 46 (2010), 450-460.

9. [9] C. Hipp, M. Taksar, Optimal non-proportional reinsurance control, Insurance: Mathematics and Economics, 47 (2010), 246-254.
10. [10] L. Gajek, D. Zagrodny, Optimal reinsurance under general risk measures, Insurance: Math. Econ., 34 (2004), 227-240.
11. [11] A. Balbas, B. Balbas, A. Heras, Optimal reinsurance with general risk measures, Insurance: Math. Econ. 44 (2009), 374-384.
12. [12] X. Zeng, Optimal reinsurance with a rescuing procedure, Insurance: Math. Econ. 46 (2010), 397-405.
13. [13] J. Cai, S.K. Tan, Optimal retention for a stop-loss reinsurance under the VaR and CTE risk measures, ASTIN Bull. 37 (1) (2007), 93-112.
14. [14] J. Cai, S.K. Tan, C. Weng, Y. Zhang, Optimal reinsurance under VaR and CTE risk measures, Insurance: Math. Econ. 43 (2008), 185-196.
15. [15] K. S. Tan, W. Chengguo, Y. Zhang, VaR and CTE criteria for optimal quota-share and stop-loss reinsurance, North Amer. Actuarial J. 13 (4) (2009), 459-482.
16. [16] Oracle, Crystal Ball 11.1.2 trial version, [Accessed December 2011].
17. [17] OptTek Systems Inc., The OptQuest Engine documentation. Available at: [Accessed December 2011].
18. [18] P. Albrecht, Risk measures, in: B. Sundt, J. Teugels, (Eds), Encyclopedia of Actuarial Science, New York: John Wiley & Sons, Ltd., 2004.
19. [19] K. Dowd, Value-at-risk, in: B Sundt, J. Teugels, (Eds), Encyclopedia of Actuarial Science, New York: John Wiley & Sons, Ltd., 2004.
20. [20] E. Tekin, I. Sabuncuoglu, Simulation optimization: A comprehensive review on theory and applications. IIE Transactions, 36 (2004), 1067–1081.
21. [21] M.C. Fu, F.W. Glover, J. April, Simulation optimization: a review, new developments, and applications, in: M.E. Kuhl, N.M. Steiger, J.A. Joines (Eds), Proceedings of the 2005 winter simulation conference, 2005.
22. [22] M.C. Fu, C.H. Chen, L. Shi, Some topics for simulation optimization, in: S. J. Mason, R. R. Hill, L. Mönch, O. Rose, T. Jefferson, J.W. Fowler, (Eds), Proceedings of the 2008 winter simulation conference, 2008.
23. [23] J. April, M. Better, F. Glover, J.P. Kelly, M. Laguna, Enhancing Business Process Management with Simulation Optimization, in: Proceedings of the 38th conference on winter simulation, 2005.