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Higher-order risk vulnerability

Author

Listed:
  • James Huang

    (Lancaster University Management School)

  • Richard Stapleton

    (Manchester Business School, Crawford House)

Abstract

We add an independent unfair background risk to higher-order risk-taking models in the current literature and examine its interaction with the main risk under consideration. Parallel to the well-known concept of risk vulnerability, which is defined by Gollier and Pratt (Econometrica 64:1109–1123, 1996), an agent is said to have a type of higher-order risk vulnerability if adding an independent unfair background risk to wealth raises his level of this type of higher-order risk aversion. We derive necessary and sufficient conditions for all types of higher-order risk vulnerabilities and explain their behavioral implications. We find that as in the case of risk vulnerability, all familiar HARA utility functions have all types of higher-order risk vulnerabilities except for a type of third-order risk vulnerability corresponding to a downside risk aversion measure called the Schwarzian derivative.

Suggested Citation

  • James Huang & Richard Stapleton, 2017. "Higher-order risk vulnerability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 387-406, February.
    • Handle: RePEc:spr:joecth:v:63:y:2017:i:2:d:10.1007_s00199-015-0935-2
    DOI: 10.1007/s00199-015-0935-2
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    References listed on IDEAS

    as
    1. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    2. Modica, Salvatore & Scarsini, Marco, 2005. "A note on comparative downside risk aversion," Journal of Economic Theory, Elsevier, vol. 122(2), pages 267-271, June.
    3. 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.
    4. Denuit, Michel M. & Eeckhoudt, Louis, 2010. "Stronger measures of higher-order risk attitudes," Journal of Economic Theory, Elsevier, vol. 145(5), pages 2027-2036, September.
    5. Keenan, Donald C & Snow, Arthur, 2002. "Greater Downside Risk Aversion," Journal of Risk and Uncertainty, Springer, vol. 24(3), pages 267-277, May.
    6. Liqun Liu & Jack Meyer, 2012. "Decreasing absolute risk aversion, prudence and increased downside risk aversion," Journal of Risk and Uncertainty, Springer, vol. 44(3), pages 243-260, June.
    7. Diamond, Peter A. & Stiglitz, Joseph E., 1974. "Increases in risk and in risk aversion," Journal of Economic Theory, Elsevier, vol. 8(3), pages 337-360, July.
    8. Guenter Franke & Richard Stapleton & Marti Subrahmanyam, 2004. "Background risk and the demand for state-contingent claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(2), pages 321-335, January.
    9. Keenan, Donald C. & Snow, Arthur, 2009. "Greater downside risk aversion in the large," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1092-1101, May.
    10. John Y. Campbell, 2006. "Household Finance," Journal of Finance, American Finance Association, vol. 61(4), pages 1553-1604, August.
    11. Günter Franke & Harris Schlesinger & Richard C. Stapleton, 2006. "Multiplicative Background Risk," Management Science, INFORMS, vol. 52(1), pages 146-153, January.
    12. Caballe, Jordi & Pomansky, Alexey, 1996. "Mixed Risk Aversion," Journal of Economic Theory, Elsevier, vol. 71(2), pages 485-513, November.
    13. W. Chiu & Louis Eeckhoudt & Beatrice Rey, 2012. "On relative and partial risk attitudes: theory and implications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 151-167, May.
    14. W. Henry Chiu, 2005. "Skewness Preference, Risk Aversion, and the Precedence Relations on Stochastic Changes," Management Science, INFORMS, vol. 51(12), pages 1816-1828, December.
    15. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    16. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-154, January.
    17. James Huang & Richard Stapleton, 2014. "Cautiousness, Skewness Preference, and the Demand for Options," Review of Finance, European Finance Association, vol. 18(6), pages 2375-2395.
    18. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-932, December.
    19. Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2011. "Effects of background risks on cautiousness with an application to a portfolio choice problem," Journal of Economic Theory, Elsevier, vol. 146(1), pages 346-358, January.
    20. Donald Keenan & Arthur Snow, 2012. "The Schwarzian derivative as a ranking of downside risk aversion," Journal of Risk and Uncertainty, Springer, vol. 44(2), pages 149-160, April.
    21. Jindapon, Paan & Neilson, William S., 2007. "Higher-order generalizations of Arrow-Pratt and Ross risk aversion: A comparative statics approach," Journal of Economic Theory, Elsevier, vol. 136(1), pages 719-728, September.
    22. W Henry Chiu, 2010. "Skewness Preference, Risk Taking and Expected Utility Maximisation," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 35(2), pages 108-129, December.
    23. Michel M. Denuit & Louis Eeckhoudt, 2010. "A General Index of Absolute Risk Attitude," Management Science, INFORMS, vol. 56(4), pages 712-715, April.
    24. Keenan, Donald C. & Snow, Arthur, 2010. "Greater prudence and greater downside risk aversion," Journal of Economic Theory, Elsevier, vol. 145(5), pages 2018-2026, September.
    25. 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.
    26. Lajeri-Chaherli, Fatma, 2004. "Proper prudence, standard prudence and precautionary vulnerability," Economics Letters, Elsevier, vol. 82(1), pages 29-34, January.
    27. David Crainich & Louis Eeckhoudt, 2008. "On the intensity of downside risk aversion," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 267-276, June.
    28. Ilia Tsetlin & Robert L. Winkler, 2005. "Risky Choices and Correlated Background Risk," Management Science, INFORMS, vol. 51(9), pages 1336-1345, September.
    29. 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.
    30. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    31. John Quiggin, 2003. "Background risk in generalized expected utility theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(3), pages 607-611, October.
    32. Louis Eeckhoudt & Christian Gollier, 2005. "The impact of prudence on optimal prevention," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 989-994, November.
    33. Liu, Liqun & Meyer, Jack, 2013. "Substituting one risk increase for another: A method for measuring risk aversion," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2706-2718.
    34. 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.
    35. 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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    More about this item

    Keywords

    Background risk; Downside risk aversion; Downside risk vulnerability; Higher-order risk vulnerability;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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