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Correlated risks, bivariate utility and optimal choices

  • DENUIT, Michel M.

    (UNIVERSITE CATHOLIQUE DE LOUVAIN,)

  • EECKHOUDT, Louis

    ()

    (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

  • MENEGATTI, Mario

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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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2009007.

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Date of creation: 01 Feb 2009
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Handle: RePEc:cor:louvco:2009007
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  1. 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.
  2. Christophe Courbage & Béatrice Rey, 2007. "Precautionary saving in the presence of other risks," Economic Theory, Springer, vol. 32(2), pages 417-424, August.
  3. Mario Menegatti, 2009. "Precautionary saving in the presence of other risks: a comment," Economic Theory, Springer, vol. 39(3), pages 473-476, June.
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  5. Mario Menegatti, 2009. "Optimal saving in the presence of two risks," Journal of Economics, Springer, vol. 96(3), pages 277-288, April.
  6. EECKHOUDT, Louis & Christian GOLLIER & Harris SCHLESINGER, 1994. "Changes in Background Risk and Risk Taking Behavior," Working Papers 005, Risk and Insurance Archive.
  7. 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.
  8. Menegatti, Mario, 2001. "On the Conditions for Precautionary Saving," Journal of Economic Theory, Elsevier, vol. 98(1), pages 189-193, May.
  9. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2007. "A Good Sign for Multivariate Risk Taking," Management Science, INFORMS, vol. 53(1), pages 117-124, January.
  10. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
  11. 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.
  12. 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).
  13. 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.
  14. Ekern, Steinar, 1980. "Increasing Nth degree risk," Economics Letters, Elsevier, vol. 6(4), pages 329-333.
  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. 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.
  17. 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.
  18. 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.
  19. Sandmo, Agnar, 1970. "The Effect of Uncertainty on Saving Decisions," Review of Economic Studies, Wiley Blackwell, vol. 37(3), pages 353-60, July.
  20. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
  21. repec:hal:journl:hal-00326101 is not listed on IDEAS
  22. repec:cor:louvrp:-2207 is not listed on IDEAS
  23. 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.
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