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Optimal risk transfer for agents with germs

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  • Li, Peng
  • Lim, Andrew E.B.
  • Shanthikumar, J. George

Abstract

We introduce a new class of risk measures called generalized entropic risk measures (GERMS) that allow economic agents to have different attitudes towards different sources of risk. We formulate the problem of optimal risk transfer in terms of these risk measures and characterize the optimal transfer contract. The optimal contract involves what we call intertemporal source-dependent quotient sharing, where agents linearly share changes in the aggregate risk reserve that occur in response to shocks to the system over time, with scaling coefficients that depend on the attitudes of each agent towards the source of risk causing the shock. Generalized entropic risk measures are not dilations of a common base risk measure, so our results extend the class of risk measures for which explicit characterizations of the optimal transfer contract can be found.

Suggested Citation

  • Li, Peng & Lim, Andrew E.B. & Shanthikumar, J. George, 2010. "Optimal risk transfer for agents with germs," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 1-12, August.
    • Handle: RePEc:eee:insuma:v:47:y:2010:i:1:p:1-12
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    References listed on IDEAS

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    1. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    2. Goovaerts, Marc J. & Laeven, Roger J.A., 2008. "Actuarial risk measures for financial derivative pricing," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 540-547, April.
    3. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A. & Tang, Qihe, 2004. "A comonotonic image of independence for additive risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 581-594, December.
    4. Burgert, Christian & Rüschendorf, Ludger, 2008. "Allocation of risks and equilibrium in markets with finitely many traders," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 177-188, February.
    5. E. Jouini & W. Schachermayer & N. Touzi, 2008. "Optimal Risk Sharing For Law Invariant Monetary Utility Functions," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 269-292, April.
    6. Bühlmann, Hans & Jewell, William S., 1979. "Optimal Risk Exchanges," ASTIN Bulletin, Cambridge University Press, vol. 10(3), pages 243-262, December.
    7. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, April.
    8. Deprez, Olivier & Gerber, Hans U., 1985. "On convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 4(3), pages 179-189, July.
    9. Bühlmann, Hans, 1984. "The General Economic Premium Principle," ASTIN Bulletin, Cambridge University Press, vol. 14(1), pages 13-21, April.
    10. Burgert Christian & Rüschendorf Ludger, 2006. "On the optimal risk allocation problem," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-19, July.
    11. Gerber, Hans U., 1978. "Pareto-Optimal Risk Exchanges and Related Decision Problems," ASTIN Bulletin, Cambridge University Press, vol. 10(1), pages 25-33, May.
    12. Borch, Karl, 1960. "Reciprocal Reinsurance Treaties," ASTIN Bulletin, Cambridge University Press, vol. 1(4), pages 170-191, December.
    13. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    14. repec:dau:papers:123456789/361 is not listed on IDEAS
    15. Barrieu, Pauline & El Karoui, Nicole, 2005. "Inf-convolution of risk measures and optimal risk transfer," LSE Research Online Documents on Economics 2829, London School of Economics and Political Science, LSE Library.
    16. David Heath & Hyejin Ku, 2004. "Pareto Equilibria with coherent measures of risk," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 163-172, April.
    17. Damir Filipović & Michael Kupper, 2008. "Optimal Capital And Risk Transfers For Group Diversification," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 55-76, January.
    18. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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    Cited by:

    1. Katsoulacos, Yannis & Ulph, David, 2017. "Regulatory decision errors, Legal Uncertainty and welfare: A general treatment," International Journal of Industrial Organization, Elsevier, vol. 53(C), pages 326-352.

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