Mean-variance optimal local reinsurance contracts

• Autorzy: Kałuszka M.
• Języki publikacji: EN

Abstrakty

EN

Reinsurance reduces the risk but it also reduces the potential profit. The aim of the paper is to derive optimal local reinsurance contracts balancing the risk measured by variance and expected profits under various mean-variance premium principles of the reinsurer. The reinsurer's premium is calculated per claim. It is found that the optimal rules are combinations of excess of loss and quota share contracts.

Słowa kluczowe

EN

reinsurance; optimal reinsurance contracts; quota share; excess of loss

PL

reasekuracja; kontrakt optymalnej reasekuracji; udział kwotowy; nadmiar strat

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2003
• Tom: Vol. 32, no 4
• Strony: 883--896
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Kałuszka M.

• Institute of Mathematics Technical University of Łódź, Żwirki 36, 90-924 Łódź, Poland

Bibliografia

• Buhlmann, H. (1996) Mathematical Methods in Risk Theory. Springer-Verlag, Berlin.
• Centeno, M.L. (1985) On combining quota-share and excess of loss. ASTIN Bulletin 15, 49-63.
• Centeno, M.L. (1986) Some mathematical aspects of combining proportional and non-proportional reinsurance. In: M. Goovaerts et al., eds., Insurance and Risk Theory. D. Reidel Publishing Company, 247-266.
• Centeno, M.L. and Sim ̃oes, O. (1991) Combining quota-share and excess of loss treaties on the reinsurance of n independent risks. ASTIN Bulletin 21, 41-55.
• Daykin, C.D., Pentikinen, T. and Pesonen, M. (1993) Practical Risk Theory for Actuaries. Chapman & Hall, London.
• De Vylder, F. and Goovaerts, M. (1999) Solvency margins and equalization reserves. Insurance: Mathematics and Economics 24, 103-115.
• Dickson, D.C.M. and Waters, H.R. (1997) Relative reinsurance retention levels. ASTIN Bulletin 27, 207-227.
• Embrechts, P., Kl ̈uppelberg, C., and Mikosch, T. (1997) Modelling Extremal Events. Springer, Berlin.
• Gajek, L. and Zagrodny, D. (2000) Insurer’s optimal reinsurance strategies. Insurance: Mathematics and Economics 27, 105-112.
• Gerathewohl, K. (1980) Reinsurance Principles and Practice. Verlag Versicherungswirtschaft, Karlsruhe.
• Gerber, H.U. (1979) An Introduction to Mathematical Risk Theory. S.S. Huebner Foundation Monographs. University of Pennsylvania.
• Goovaerts, M.J., De Vylder, F., and Haezendonck, J. (1984) Insurance Premiums. North-Holland, Amsterdam
• Davis, M.H.A. and Karatzas, I. (1994) A deterministic approach to optimal stopping Probability. F.P. Kelly, ed., Statistics and Optimisation. John Wiley & Sons, 1994, 455 – 466.
• Hart, D.G., Buchanan, R.A., and Howe, B.A. (1996) The Actuarial Practice of General Insurance. Institute of Actuaries of Australia, Sydney.
• Hesselager, O. (1990) Some results on optimal reinsurance in terms of the adjustment coefficient. Scandinavian Actuarial Journal, 80-95.
• Kahn, P.M. (1961) Some remarks on a recent paper of Borch. ASTIN Bulletin 5, 265-272
• Kaluszka, M. (2001) Optimal reinsurance under mean-variance premium principles. Insurance: Mathematics and Economics 28, 61-67.
• Kaluszka, M. (2004) Mean-variance optimal reinsurance agreements. Scandinavian Actuarial Journal (in press).
• Koller, B. and Dettwyler, N. (1997) APS reinsurance. ASTIN Bulletin 27, 329-337.
• Mazur, T. (2000) Risk management in reinsurance process. Ph.D. Dissertation, Technical University of Lodz (in Polish).
• Lehrke, T. A. (1997) Aggregate excess or stop-loss reinsurance. Reinsurance 1997, Strain Publishing & Seminars, 244-278.
• Pesonen, M.I. (1984) Optimal reinsurances. Scandinavian Actuarial Journal, 65-90.
• Rolski, T., Schmidli, H., Schmidt, V. and Teugels, J. (1998) Stochastic Processes for Insurance and Finance. J.Wiley & Sons, Chichester.
• Samson, D. (1985) Expected utility strategic decision models for general insurers. ASTIN Bulletin 16, 46-58.
• Schnieper, R. (2000) Portfolio optimization. ASTIN Bulletin 30, 195-248.
• Schmitter, H. (2001) Setting optimal reinsurance retentions. Swiss Re Publications.
• Straub, E. (1988) Non-Life Insurance Mathematics. Springer, Berlin.