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Correlated risks, bivariate utility and optimal choices

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  • Michel Denuit

    ()

  • Louis Eeckhoudt

    ()

  • Mario Menegatti

    ()

Abstract

In this paper, we consider a décision-maker facing a financial risk flanked by a background risk, possibly non-financial, such as health or environmental risk. A decision has to be made about the amount of an investment (in the financial dimension) resulting in a future benefit either in the same dimension (savings) or in the order dimension (environmental quality or health improvement). In the first case, we show that the optimal amount of savings decreases as the pair of risks increases in the bivariate increasing concave dominance rules of higher degrees which express the common preferences of all the decision-makers whose two-argument utility function possesses direct and cross derivatives fulfilling some specific requirements. Roughly speaking, the optimal amount of savings decreases as the two risks become "less positively correlated" or marginally improve in univariate stochastic dominance. In the second case, a similar conclusion on optimal investment is reached under alternative conditions on the derivatives of the utility function.

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 46 (2011)
Issue (Month): 1 (January)
Pages: 39-54

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Handle: RePEc:spr:joecth:v:46:y:2011:i:1:p:39-54

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Related research

Keywords: Precautionary savings; Background risk; Bivariate higher order increasing concave stochastic dominance; Risks correlation; D81; E21;

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References

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  1. 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.
  2. Denuit, Michel & Lefevre, Claude & Mesfioui, M'hamed, 1999. "A class of bivariate stochastic orderings, with applications in actuarial sciences," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 31-50, March.
  3. EECKHOUDT, Louis & Christian GOLLIER & Harris SCHLESINGER, 1994. "Changes in Background Risk and Risk Taking Behavior," Working Papers 005, Risk and Insurance Archive.
  4. 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.
  5. Denuit, Michel & Vylder, Etienne De & Lefevre, Claude, 1999. "Extremal generators and extremal distributions for the continuous s-convex stochastic orderings," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 201-217, May.
  6. 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.
  7. Eeckhoudt, Louis & Schlesinger, Harris, 2008. "Changes in risk and the demand for saving," Journal of Monetary Economics, Elsevier, vol. 55(7), pages 1329-1336, October.
  8. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2006. "A Good Sign for Multivariate Risk Taking," CESifo Working Paper Series 1796, CESifo Group Munich.
  9. Menegatti, Mario, 2001. "On the Conditions for Precautionary Saving," Journal of Economic Theory, Elsevier, vol. 98(1), pages 189-193, May.
  10. Christophe Courbage & Béatrice Rey, 2007. "Precautionary saving in the presence of other risks," Economic Theory, Springer, vol. 32(2), pages 417-424, August.
  11. Atkinson, Anthony B & Bourguignon, Francois, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Wiley Blackwell, vol. 49(2), pages 183-201, April.
  12. Ekern, Steinar, 1980. "Increasing Nth degree risk," Economics Letters, Elsevier, vol. 6(4), pages 329-333.
  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. Sandmo, Agnar, 1970. "The Effect of Uncertainty on Saving Decisions," Review of Economic Studies, Wiley Blackwell, vol. 37(3), pages 353-60, July.
  15. 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.
  16. repec:cor:louvrp:2207 is not listed on IDEAS
  17. Thomas Eichner & Andreas Wagener, 2003. "Variance Vulnerability, Background Risks, and Mean-Variance Preferences," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 28(2), pages 173-184, December.
  18. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
  19. Miles S. Kimball, 1991. "Standard Risk Aversion," NBER Technical Working Papers 0099, National Bureau of Economic Research, Inc.
  20. Mario Menegatti, 2009. "Optimal saving in the presence of two risks," Journal of Economics, Springer, vol. 96(3), pages 277-288, April.
  21. DENUIT, Michel & EECKHOUDT, Louis & REY, Béatrice, . "Some consequences of correlation aversion in decision science," CORE Discussion Papers RP -2207, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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