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Increased Risk-Bearing with Background Risk

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Author Info
Christian Gollier (U of Toulouse)
Edward Schlee (Arizona State University)

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Abstract

Analyses of risk-bearing often assume that agents face only one risk. Agents however usually face several risks and the interaction between them can affect the willingness to bear any one of them. We consider how the introduction of background risk affects the comparative statics predictions of distribution changes in the standard two asset portfolio model. We show that such predictions are fairly robust, no matter what the correlation between the two risks. We consider changes in the conditional distributions of the risky asset's return; and changes in the marginal distribution of the asset's return. For the first question, a version of Gollier's (1995) Central Riskiness order is sufficient and necessary to increase risk-bearing. For the second question, Monotone Likelihood Ratio improvements are sufficient and necessary. Many of our proofs illustrate the "basis" approach to comparative statics under uncertainty.

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Publisher Info
Article provided by Berkeley Electronic Press in its journal Topics in Theoretical Economics.

Volume (Year): 6 (2006)
Issue (Month): 1 ()
Pages: 1249-1249
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Handle: RePEc:bep:thetop:v:6:y:2006:i:1:p:1249-1249

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Related research
Keywords: Comparative statics uncertainty risk-bearing background risk monotone likelihood ratio order central riskiness single-crossing property multivariate risk

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-23, September. [Downloadable!] (restricted)
  2. EECKHOUDT, Louis & Christian GOLLIER & Harris SCHLESINGER, 1994. "Changes in Background Risk and Risk Taking Behavior," Working Papers 005, Risk and Insurance Archive. [Downloadable!]
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  3. Ormiston, Michael B & Schlee, Edward E, 2001. "Mean-Variance Preferences and Investor Behaviour," Economic Journal, Royal Economic Society, vol. 111(474), pages 849-61, October. [Downloadable!] (restricted)
  4. Gollier, Christian, 1997. "A Note on Portfolio Dominance," Review of Economic Studies, Blackwell Publishing, vol. 64(1), pages 147-50, January. [Downloadable!] (restricted)
  5. Eeckhoudt, Louis & Gollier, Christian, 1995. "Demand for Risky Assets and the Monotone Probability Ratio Order," Journal of Risk and Uncertainty, Springer, vol. 11(2), pages 113-22, September.
  6. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March. [Downloadable!] (restricted)
  7. Susan Athey, 2002. "Monotone Comparative Statics Under Uncertainty," The Quarterly Journal of Economics, MIT Press, vol. 117(1), pages 187-223, February. [Downloadable!] (restricted)
  8. 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 621-38, May. [Downloadable!] (restricted)
  9. Hadar, Josef & Seo, Tae Kun, 1990. "The Effects of Shifts in a Return Distribution on Optimal Portfolios," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 721-36, August. [Downloadable!] (restricted)
  10. Dionne, G. & Gollier, C., 1996. "A Model Of Comparative Statics For Changes in Stochastic Returns With Dependent Risky Assets," Papers 96.420, Toulouse - GREMAQ.
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  11. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn. [Downloadable!] (restricted)
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  12. Kihlstrom, Richard E & Romer, David & Williams, Steve, 1981. "Risk Aversion with Random Initial Wealth," Econometrica, Econometric Society, vol. 49(4), pages 911-20, June. [Downloadable!] (restricted)
  13. Meyer, Jack & Ormiston, Michael B, 1994. "The Effect on Optimal Portfolios of Changing the Return to a Risky Asset: The Case of Dependent Risky Returns," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 603-12, August. [Downloadable!] (restricted)
  14. Gollier Christian, 1995. "The Comparative Statics of Changes in Risk Revisited," Journal of Economic Theory, Elsevier, vol. 66(2), pages 522-535, August. [Downloadable!] (restricted)
  15. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May. [Downloadable!] (restricted)
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  16. Jewitt, Ian, 1987. "Risk Aversion and the Choice between Risky Prospects: The Preservation of Comparative Statics Results," Review of Economic Studies, Blackwell Publishing, vol. 54(1), pages 73-85, January. [Downloadable!] (restricted)
  17. Heaton, John & Lucas, Deborah, 2000. "Portfolio Choice in the Presence of Background Risk," Economic Journal, Royal Economic Society, vol. 110(460), pages 1-26, January. [Downloadable!] (restricted)
  18. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March. [Downloadable!] (restricted)
  19. Meyer, Jack & Ormiston, Michael B, 1985. "Strong Increases in Risk and Their Comparative Statics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(2), pages 425-37, June. [Downloadable!] (restricted)
  20. Nachman, David C., 1982. "Preservation of "more risk averse" under expectations," Journal of Economic Theory, Elsevier, vol. 28(2), pages 361-368, December. [Downloadable!] (restricted)
  21. Ormiston Michael B. & Schlee Edward E., 1993. "Comparative Statics under Uncertainty for a Class of Economic Agents," Journal of Economic Theory, Elsevier, vol. 61(2), pages 412-422, December. [Downloadable!] (restricted)
  22. Cheng, Hsueh-Cheng & Magill, Michael J P & Shafer, Wayne J, 1987. "Some Results on Comparative Statics under Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(2), pages 493-507, June. [Downloadable!] (restricted)
  23. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-54, January. [Downloadable!] (restricted)
  24. Edward Schlee & Christian Gollier, . "Increased Risk-Bearing with Background Risk," Working Papers 2132848, Department of Economics, W. P. Carey School of Business, Arizona State University. [Downloadable!]
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  25. Athey, S., 1996. "Characterizing Properties of Stochastic Objective Functions," Working papers 96-1, Massachusetts Institute of Technology (MIT), Department of Economics.
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  1. Christian Gollier & Edward Schlee, 2006. "Increased Risk-Bearing with Background Risk," Topics in Theoretical Economics, Berkeley Electronic Press, vol. 6(1), pages 1249-1249. [Downloadable!] (restricted)
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