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Risk aversion with two risks: A theoretical extension

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  • Li, Jingyuan
  • Liu, Dongri
  • Wang, Jianli

Abstract

We identify new conditions ensuring risk aversion in the sense of Arrow–Pratt in a two-argument utility framework in which a financial risk is accompanied by a background risk. Our results generalize the findings of Finkelshtain et al. (1999). We consider a sequence of possible dependence among risks. We also provide an empirical example showing that second-order expectation dependence cannot be ignored in determining risk aversion with two risks.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:mateco:v:63:y:2016:i:c:p:100-105
    DOI: 10.1016/j.jmateco.2016.01.002
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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. Cary Deck & Harris Schlesinger, 2010. "Exploring Higher Order Risk Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(4), pages 1403-1420.
    3. Béatrice Rey, 2003. "A Note on Optimal Insurance in the presence of a Nonpecuniary Background Risk," Theory and Decision, Springer, vol. 54(1), pages 73-83, February.
    4. Cary Deck & Harris Schlesinger, 2014. "Consistency of Higher Order Risk Preferences," Econometrica, Econometric Society, vol. 82, pages 1913-1943, September.
    5. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    6. Béatrice Rey, 2003. "A Note on Optimal Insurance in the presence of a Nonpecuniary Background Risk," Post-Print halshs-03352991, HAL.
    7. Eeckhoudt, Louis & Schlesinger, Harris & Tsetlin, Ilia, 2009. "Apportioning of risks via stochastic dominance," Journal of Economic Theory, Elsevier, vol. 144(3), pages 994-1003, May.
    8. Franke, Guenter & Schlesinger, Harris & Stapleton, Richard C., 2011. "Risk taking with additive and multiplicative background risks," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1547-1568, July.
    9. Pratt, John W, 1988. "Aversion to One Risk in the Presence of Others," Journal of Risk and Uncertainty, Springer, vol. 1(4), pages 395-413, December.
    10. Xuehu Zhu & Xu Guo & Lu Lin & Lixing Zhu, 2016. "Testing for positive expectation dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 135-153, February.
    11. Ilia Tsetlin & Robert L. Winkler, 2005. "Risky Choices and Correlated Background Risk," Management Science, INFORMS, vol. 51(9), pages 1336-1345, September.
    12. Eeckhoudt, Louis & Gollier, Christian & Schlesinger, Harris, 1996. "Changes in Background Risk and Risk-Taking Behavior," Econometrica, Econometric Society, vol. 64(3), pages 683-689, May.
    13. Ross, Stephen A, 1981. "Some Stronger Measures of Risk Aversion in the Small and the Large with Applications," Econometrica, Econometric Society, vol. 49(3), pages 621-638, May.
    14. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2007. "A Good Sign for Multivariate Risk Taking," Management Science, INFORMS, vol. 53(1), pages 117-124, January.
    15. 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.
    16. Michel Denuit & Rachel Huang & Larry Tzeng, 2015. "Almost expectation and excess dependence notions," Theory and Decision, Springer, vol. 79(3), pages 375-401, November.
    17. Kihlstrom, Richard E & Romer, David & Williams, Steve, 1981. "Risk Aversion with Random Initial Wealth," Econometrica, Econometric Society, vol. 49(4), pages 911-920, June.
    18. 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.
    19. Günter Franke & Harris Schlesinger & Richard C. Stapleton, 2006. "Multiplicative Background Risk," Management Science, INFORMS, vol. 52(1), pages 146-153, January.
    20. Pratt, John W, 1990. "The Logic of Partial-Risk Aversion: Paradox Lost," Journal of Risk and Uncertainty, Springer, vol. 3(2), pages 105-113, June.
    21. Kit Wong, 2014. "Hedging and the competitive firm under correlated price and background risk," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 329-340, October.
    22. Kit Pong Wong, 2013. "Cross Hedging with Currency Forward Contracts," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(7), pages 653-674, July.
    23. Udo Broll & Peter Welzel & Kit Wong, 2015. "Futures hedging with basis risk and expectation dependence," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 62(3), pages 213-221, September.
    24. Cuadras, C. M., 2002. "On the Covariance between Functions," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 19-27, April.
    25. Jokung, Octave, 2011. "Risk apportionment via bivariate stochastic dominance," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 448-452.
    26. Dionne, Georges & Li, Jingyuan, 2014. "When can expected utility handle first-order risk aversion?," Journal of Economic Theory, Elsevier, vol. 154(C), pages 403-422.
    27. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-1123, September.
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    Cited by:

    1. 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.
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    3. Christophe Muller, 2019. "Social Shock Sharing and Stochastic Dominance," Working Papers halshs-02005735, HAL.
    4. Wong, Kit Pong, 2021. "Comparative risk aversion with two risks," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    5. He, Junnan & Tang, Qihe & Zhang, Huan, 2016. "Risk reducers in convex order," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 80-88.
    6. Wong, Kit Pong, 2022. "Diversification and risk attitudes toward two risks," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    7. 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.
    8. Crainich, David & Eeckhoudt, Louis & Courtois, Olivier Le, 2020. "Intensity of preferences for bivariate risk apportionment," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 153-160.
    9. 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).

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