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Optimal reinsurance policy: The adjustment coefficient and the expected utility criteria

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  • Guerra, Manuel
  • de Lourdes Centeno, Maria

Abstract

This paper is concerned with the optimal form of reinsurance from the ceding company point of view, when the cedent seeks to maximize the adjustment coefficient of the retained risk. We deal with the problem by exploring the relationship between maximizing the adjustment coefficient and maximizing the expected utility of wealth for the exponential utility function, both with respect to the retained risk of the insurer. Assuming that the premium calculation principle is a convex functional and that some other quite general conditions are fulfilled, we prove the existence and uniqueness of solutions and provide a necessary optimal condition. These results are used to find the optimal reinsurance policy when the reinsurance premium calculation principle is the expected value principle or the reinsurance loading is an increasing function of the variance. In the expected value case the optimal form of reinsurance is a stop-loss contract. In the other cases, it is described by a nonlinear function.

Suggested Citation

  • Guerra, Manuel & de Lourdes Centeno, Maria, 2008. "Optimal reinsurance policy: The adjustment coefficient and the expected utility criteria," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 529-539, April.
  • Handle: RePEc:eee:insuma:v:42:y:2008:i:2:p:529-539
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    References listed on IDEAS

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    1. Deprez, Olivier & Gerber, Hans U., 1985. "On convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 4(3), pages 179-189, July.
    2. Centeno, Maria de Lourdes, 1997. "Excess of Loss Reinsurance and the Probability of Ruin in Finite Horizon," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 27(01), pages 59-70, May.
    3. Vajda, Stefan, 1962. "Minimum Variance Reinsurance," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 2(02), pages 257-260, September.
    4. Ohlin, Jan, 1969. "On a class of measures of dispersion with application to optimal reinsurance," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 5(02), pages 249-266, May.
    5. Kahn, Paul Markham, 1961. "Some Remarks on a Recent Paper by Borch," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 1(05), pages 265-272, July.
    6. anonymous, 1991. "Fed upgrades functional cost analysis program," Financial Update, Federal Reserve Bank of Atlanta, issue Win, pages 1-2,6.
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    Citations

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    Cited by:

    1. Belzunce, Félix & Suárez-Llorens, Alfonso & Sordo, Miguel A., 2012. "Comparison of increasing directionally convex transformations of random vectors with a common copula," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 385-390.
    2. Cheung, K.C. & Chong, W.F. & Yam, S.C.P., 2015. "The optimal insurance under disappointment theories," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 77-90.
    3. Lu, ZhiYi & Meng, LiLi & Wang, Yujin & Shen, Qingjie, 2016. "Optimal reinsurance under VaR and TVaR risk measures in the presence of reinsurer’s risk limit," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 92-100.
    4. Centeno, M.L. & Guerra, M., 2010. "The optimal reinsurance strategy -- the individual claim case," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 450-460, June.
    5. Begoña Fernández & Daniel Hernández-Hernández & Ana Meda & Patricia Saavedra, 2008. "An optimal investment strategy with maximal risk aversion and its ruin probability," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 159-179, August.
    6. Asimit, Alexandru V. & Badescu, Alexandru M. & Haberman, Steven & Kim, Eun-Seok, 2016. "Efficient risk allocation within a non-life insurance group under Solvency II Regime," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 69-76.
    7. repec:spr:compst:v:68:y:2008:i:1:p:159-179 is not listed on IDEAS
    8. Asimit, Alexandru V. & Badescu, Alexandru M. & Verdonck, Tim, 2013. "Optimal risk transfer under quantile-based risk measurers," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 252-265.
    9. repec:spr:mathme:v:85:y:2017:i:2:d:10.1007_s00186-016-0559-8 is not listed on IDEAS
    10. repec:eee:insuma:v:76:y:2017:i:c:p:48-55 is not listed on IDEAS
    11. Dimitrova, Dimitrina S. & Kaishev, Vladimir K., 2010. "Optimal joint survival reinsurance: An efficient frontier approach," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 27-35, August.
    12. Asimit, Alexandru V. & Chi, Yichun & Hu, Junlei, 2015. "Optimal non-life reinsurance under Solvency II Regime," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 227-237.
    13. Guerra, Manuel & Centeno, M.L., 2012. "Are quantile risk measures suitable for risk-transfer decisions?," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 446-461.
    14. Asimit, Alexandru V. & Badescu, Alexandru M. & Cheung, Ka Chun, 2013. "Optimal reinsurance in the presence of counterparty default risk," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 690-697.
    15. Lu, ZhiYi & Liu, LePing & Meng, ShengWang, 2013. "Optimal reinsurance with concave ceded loss functions under VaR and CTE risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 46-51.
    16. Badaoui, Mohamed & Fernández, Begoña, 2013. "An optimal investment strategy with maximal risk aversion and its ruin probability in the presence of stochastic volatility on investments," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 1-13.

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