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Ross risk vulnerability for introductions and changes in background risk

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  • Keenan, Donald C.
  • Snow, Arthur

Abstract

We present two theorems that provide necessary and sufficient conditions for an expected utility maximizer to become more risk averse in the sense of Ross with respect to bearing a foreground risk after the introduction of any independent fair or unfair additive background risk. We call these decision makers Ross risk vulnerable, and show that Ross decreasing absolute risk aversion and Ross decreasing absolute prudence are jointly sufficient for Ross risk vulnerability. Restrictions on utility necessary and sufficient for Ross risk vulnerability with respect to stochastic dominance deteriorations of an existing background risk are also presented. Our analysis concludes with applications of Ross risk vulnerability.

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  • Keenan, Donald C. & Snow, Arthur, 2012. "Ross risk vulnerability for introductions and changes in background risk," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 197-206.
    • Handle: RePEc:eee:mateco:v:48:y:2012:i:4:p:197-206
    DOI: 10.1016/j.jmateco.2012.04.003
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    1. 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.
    2. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    3. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-154, January.
    4. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    5. Lajeri-Chaherli, Fatma, 2004. "Proper prudence, standard prudence and precautionary vulnerability," Economics Letters, Elsevier, vol. 82(1), pages 29-34, January.
    6. Bruno Jullien & Bernard Salanié & François Salanié, 2007. "Screening risk-averse agents under moral hazard: single-crossing and the CARA case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(1), pages 151-169, January.
    7. Olivier Mahul, 2000. "Optimum crop insurance under joint yield and price risk," Post-Print hal-01952116, HAL.
    8. 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.
    9. Mohamed Belhaj & Renaud Bourl?s & Fr?d?ric Dero?an, 2014. "Risk-Taking and Risk-Sharing Incentives under Moral Hazard," American Economic Journal: Microeconomics, American Economic Association, vol. 6(1), pages 58-90, February.
    10. Carroll, Christopher D & Kimball, Miles S, 1996. "On the Concavity of the Consumption Function," Econometrica, Econometric Society, vol. 64(4), pages 981-992, July.
    11. 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.
    12. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    13. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(1), pages 187-223.
    14. Martin Gaynor & Paul Gertler, 1995. "Moral Hazard and Risk Spreading in Partnerships," RAND Journal of Economics, The RAND Corporation, vol. 26(4), pages 591-613, Winter.
    15. Dutta, Prajit K. & Radner, Roy, 1994. "Moral hazard," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 26, pages 869-903, Elsevier.
    16. Gregory M. Gelles & Douglas W. Mitchell, 1999. "Broadly Decreasing Risk Aversion," Management Science, INFORMS, vol. 45(10), pages 1432-1439, October.
    17. Denuit, Michel & Eeckhoudt, Louis, 2010. "Stronger measures of higher-order risk attitudes," LIDAM Discussion Papers ISBA 2010010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    18. Atanu Saha, 1993. "Expo-Power Utility: A ‘Flexible’ Form for Absolute and Relative Risk Aversion," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 75(4), pages 905-913.
    19. 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.
    20. Christian Gollier, 2004. "The Economics of Risk and Time," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262572249, December.
    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. Israel Finkelshtain & James A. Chalfant, 1993. "Portfolio Choices in the Presence of Other Risks," Management Science, INFORMS, vol. 39(8), pages 925-936, August.
    23. Turnbull, S M, 1983. "Additional Aspects of Rational Insurance Purchasing," The Journal of Business, University of Chicago Press, vol. 56(2), pages 217-229, April.
    24. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    25. Wagener, Andreas, 2006. "Chebyshev's Algebraic Inequality and comparative statics under uncertainty," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 217-221, September.
    26. Donald Keenan & Donald Rudow & Arthur Snow, 2008. "Risk preferences and changes in background risk," Journal of Risk and Uncertainty, Springer, vol. 36(2), pages 139-152, April.
    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.
    28. Machina, Mark J & Pratt, John W, 1997. "Increasing Risk: Some Direct Constructions," Journal of Risk and Uncertainty, Springer, vol. 14(2), pages 103-127, March.
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    2. Denuit, Michel M. & Eeckhoudt, Louis & Schlesinger, Harris, 2013. "When Ross meets Bell: The linex utility function," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 177-182.
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    5. Maddalena Ferranna, 2017. "Does Inefficient Risk Sharing Increase Public Self-Protection?," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 42(1), pages 59-85, March.

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