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Preserving the Rothschild–Stiglitz type increase in risk with background risk: A characterization

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  • Denuit, Michel M.
  • Mesfioui, Mhamed

Abstract

In order to generalize previous results by Li et al. (2016), Guo et al. (2016) extended the definition of the Rothschild–Stiglitz type of increase in risk to a background risk framework. They provided several sufficient conditions for such a ranking to hold, involving expectation dependence concepts. In this short note, the corresponding characterizations are established, based on the bivariate higher-degree increasing concave orders introduced by Denuit et al. (1999).

Suggested Citation

  • Denuit, Michel M. & Mesfioui, Mhamed, 2017. "Preserving the Rothschild–Stiglitz type increase in risk with background risk: A characterization," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 1-5.
    • Handle: RePEc:eee:insuma:v:72:y:2017:i:c:p:1-5
    DOI: 10.1016/j.insmatheco.2016.10.012
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    References listed on IDEAS

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    1. Michel Denuit & Louis Eeckhoudt & Mario Menegatti, 2011. "Correlated risks, bivariate utility and optimal choices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(1), pages 39-54, January.
    2. Michel Denuit & Béatrice Rey, 2013. "Another look at risk apportionment," Post-Print halshs-03353453, HAL.
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    4. L. Eeckhoudt & M. Denuit, 2010. "Bivariate stochastic dominance and substitute risk (in) dependent utility," Post-Print hal-00572956, HAL.
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    9. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2007. "A Good Sign for Multivariate Risk Taking," Management Science, INFORMS, vol. 53(1), pages 117-124, January.
    10. Li, Jingyuan, 2011. "The demand for a risky asset in the presence of a background risk," Journal of Economic Theory, Elsevier, vol. 146(1), pages 372-391, January.
    11. Michel Denuit & Rachel Huang & Larry Tzeng, 2015. "Almost expectation and excess dependence notions," Theory and Decision, Springer, vol. 79(3), pages 375-401, November.
    12. Denuit, Michel & Mesfioui, Mhamed, 2010. "Generalized increasing convex and directionally convex orders," LIDAM Discussion Papers ISBA 2010012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Finkelshtain, Israel & Kella, Offer & Scarsini, Marco, 1999. "On risk aversion with two risks," Journal of Mathematical Economics, Elsevier, vol. 31(2), pages 239-250, March.
    14. Denuit, Michel & Rey, Beatrice, 2013. "Another look at risk apportionment," LIDAM Reprints ISBA 2013027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. Guo, Xu & Li, Jingyuan & Liu, Dongri & Wang, Jianli, 2016. "Preserving the Rothschild–Stiglitz type of increasing risk with background risk," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 144-149.
    16. Li, Jingyuan & Liu, Dongri & Wang, Jianli, 2016. "Risk aversion with two risks: A theoretical extension," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 100-105.
    17. Michel Denuit & Louis Eeckhoudt, 2010. "Bivariate Stochastic Dominance and Substitute Risk-(In)dependent Utilities," Decision Analysis, INFORMS, vol. 7(3), pages 302-312, September.
    18. Denuit, Michel & Lefevre, Claude & Mesfioui, M'hamed, 1999. "A class of bivariate stochastic orderings, with applications in actuarial sciences," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 31-50, March.
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    Cited by:

    1. Denuit, Michel & Sznajder, Dominik & Trufin, Julien, 2019. "Model selection based on Lorenz and concentration curves, Gini indices and convex order," LIDAM Discussion Papers ISBA 2019006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Denuit, Michel & Robert, Christian Y., 2020. "Conditional tail expectation decomposition and conditional mean risk sharing for dependent and conditionally independent risks," LIDAM Discussion Papers ISBA 2020018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Wong, Kit Pong, 2021. "Comparative risk aversion with two risks," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    4. Denuit, Michel & Sznajder, Dominik & Trufin, Julien, 2019. "Model selection based on Lorenz and concentration curves, Gini indices and convex order," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 128-139.
    5. Denuit, Michel & Trufin, Julien & Verdebout, Thomas, 2021. "Testing for more positive expectation dependence with application to model comparison," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 163-172.
    6. Denuit, Michel, 2019. "Size-biased risk measures of compound sums," LIDAM Discussion Papers ISBA 2019009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Denuit, Michel & Trufin, Julien & Verdebout, Thomas, 2021. "Testing for more positive expectation dependence with application to model comparison," LIDAM Discussion Papers ISBA 2021021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Michel Denuit & Christian Y. Robert, 2022. "Conditional Tail Expectation Decomposition and Conditional Mean Risk Sharing for Dependent and Conditionally Independent Losses," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1953-1985, September.

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