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Comparative Ross Risk Aversion in the Presence of Mean Dependent Risks

  • Georges Dionne
  • Jingyuan Li

This paper studies comparative risk aversion between risk averse agents in the presence of a background risk. Although the literature covers this question extensively, our contribution differs from most of the literature in two respects. First, background risk does not need to be additive or multiplicative. Second, the two risks are not necessary mean independent, and may be conditional expectation increasing or decreasing. We show that our order of cross Ross risk aversion is equivalent to the order of partial risk premium, while our index of decreasing cross Ross risk aversion is equivalent to decreasing partial risk premium. These results generalize the comparative risk aversion model developed by Ross (1981) for mean independent risks. Finally, we show that decreasing cross Ross risk aversion gives rise to the utility function family belonging to the class of n-switch utility functions.

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Paper provided by CIRPEE in its series Cahiers de recherche with number 1211.

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Date of creation: 2012
Date of revision:
Handle: RePEc:lvl:lacicr:1211
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  1. Günter Franke & Harris Schlesinger & Richard C. Stapleton, 2011. "Risk Taking with Additive and Multiplicative Background Risks," Working Paper Series of the Department of Economics, University of Konstanz 2011-25, Department of Economics, University of Konstanz.
  2. Eeckhoudt, Louis & Gollier, Christian & Schlesinger, Harris, 1996. "Changes in Background Risk and Risk-Taking Behavior," Econometrica, Econometric Society, vol. 64(3), pages 683-89, May.
  3. Li, Jingyuan, 2009. "Comparative higher-degree Ross risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 333-336, December.
  4. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  5. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2007. "A Good Sign for Multivariate Risk Taking," Management Science, INFORMS, vol. 53(1), pages 117-124, January.
  6. DENUIT, Michel M. & EECKHOUDT, Louis & MENEGATTI, Mario, . "Correlated risks, bivariate utility and optimal choices," CORE Discussion Papers RP 2272, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. 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.
  8. Scott F. Richard, 1975. "Multivariate Risk Aversion, Utility Independence and Separable Utility Functions," Management Science, INFORMS, vol. 22(1), pages 12-21, September.
  9. Weil, Philippe, 1992. "Equilibrium asset prices with undiversifiable labor income risk," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 769-790.
  10. Doherty, Neil A & Schlesinger, Harris, 1983. "The Optimal Deductible for an Insurance Policy When Initial Wealth Is Random," The Journal of Business, University of Chicago Press, vol. 56(4), pages 555-65, October.
  11. 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.
  12. Modica, Salvatore & Scarsini, Marco, 2005. "A note on comparative downside risk aversion," Journal of Economic Theory, Elsevier, vol. 122(2), pages 267-271, June.
  13. Mario Menegatti, 2009. "Precautionary saving in the presence of other risks: a comment," Economic Theory, Springer, vol. 39(3), pages 473-476, June.
  14. Doherty, Neil A. & Schlesinger, Harris, 1986. "A note on risk premiums with random initial wealth," Insurance: Mathematics and Economics, Elsevier, vol. 5(3), pages 183-185, July.
  15. Bleichrodt, Han & Crainich, David & Eeckhoudt, Louis, 2003. "Comorbidities and the willingness to pay for health improvements," Journal of Public Economics, Elsevier, vol. 87(11), pages 2399-2406, October.
  16. Gollier, Christian & Schlesinger, Harris, 2002. "Changes in risk and asset prices," Journal of Monetary Economics, Elsevier, vol. 49(4), pages 747-760, May.
  17. repec:cor:louvrp:-2361 is not listed on IDEAS
  18. Doherty, Neil A & Schlesinger, Harris, 1983. "Optimal Insurance in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 91(6), pages 1045-54, December.
  19. Kischka, Peter, 1988. "Aspects of optimal insurance demand when there are uninsurable risks," Insurance: Mathematics and Economics, Elsevier, vol. 7(1), pages 9-14, January.
  20. M. Denuit & L. Eeckhoudt & H. Schlesinger, 2013. "When ross meets bell: the linex utility function," Post-Print hal-00845936, HAL.
  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. 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.
  23. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
  24. Christophe Courbage, 2001. "On Bivariate Risk Premia," Theory and Decision, Springer, vol. 50(1), pages 29-34, February.
  25. David E. Bell, 1988. "One-Switch Utility Functions and a Measure of Risk," Management Science, INFORMS, vol. 34(12), pages 1416-1424, December.
  26. Cuadras, C. M., 2002. "On the Covariance between Functions," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 19-27, April.
  27. Israel Finkelshtain & James A. Chalfant, 1993. "Portfolio Choices in the Presence of Other Risks," Management Science, INFORMS, vol. 39(8), pages 925-936, August.
  28. 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.
  29. Mario Menegatti, 2009. "Optimal saving in the presence of two risks," Journal of Economics, Springer, vol. 96(3), pages 277-288, April.
  30. Marco Scarsini & Israel Finkelshtain & Offer Kella, 1999. "On risk aversion with two risks," Post-Print hal-00540256, HAL.
  31. Christophe Courbage & Béatrice Rey, 2007. "Precautionary saving in the presence of other risks," Economic Theory, Springer, vol. 32(2), pages 417-424, August.
  32. Nachman, David C., 1982. "Preservation of "more risk averse" under expectations," Journal of Economic Theory, Elsevier, vol. 28(2), pages 361-368, December.
  33. Pratt, John W, 1990. " The Logic of Partial-Risk Aversion: Paradox Lost," Journal of Risk and Uncertainty, Springer, vol. 3(2), pages 105-13, June.
  34. DENUIT, Michel & EECKHOUDT, Louis, . "Bivariate stochastic dominance and substitute risk-(in)dependent utilities," CORE Discussion Papers RP 2361, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  35. Larry G. Epstein & Stephen M. Tanny, 1980. "Increasing Generalized Correlation: A Definition and Some Economic Consequences," Canadian Journal of Economics, Canadian Economics Association, vol. 13(1), pages 16-34, February.
  36. Ilia Tsetlin & Robert L. Winkler, 2012. "Multiattribute One-Switch Utility," Management Science, INFORMS, vol. 58(3), pages 602-605, March.
  37. Franke, Günter & Schlesinger, Harris & Stapleton, Richard C., 2002. "Multiplicative background risk," Discussion Papers, various Research Units FS IV 02-06, Social Science Research Center Berlin (WZB).
  38. Ilia Tsetlin & Robert L. Winkler, 2009. "Multiattribute Utility Satisfying a Preference for Combining Good with Bad," Management Science, INFORMS, vol. 55(12), pages 1942-1952, December.
  39. 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.
  40. Marco Scarsini, 1988. "Dominance Conditions for Multivariate Utility Functions," Post-Print hal-00542237, HAL.
  41. David E. Bell & Peter C. Fishburn, 2001. "Strong One-Switch Utility," Management Science, INFORMS, vol. 47(4), pages 601-604, April.
  42. Ilia Tsetlin & Robert L. Winkler, 2005. "Risky Choices and Correlated Background Risk," Management Science, INFORMS, vol. 51(9), pages 1336-1345, September.
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