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Multiplicative Background Risk

  • Günter Franke

    ()

    (University of Konstanz, Fach D147, 78457 Konstanz, Germany)

  • Harris Schlesinger

    ()

    (Department of Economics and Finance, 200 Alston Hall, University of Alabama, Tuscaloosa, Alabama 35487-0224)

  • Richard C. Stapleton

    ()

    (University of Manchester, Crawford House, Oxford Road, Manchester, M13 9PL, England)

Although there has been much attention in recent years on the effects of additive background risks, the same is not true for its multiplicative counterpart. We consider random wealth of the multiplicative form x\~y\~, where x\~ and y\~ are statistically independent random variables. We assume that x\~ is endogenous to the economic agent but that y\~ is an exogenous and nontradable background risk that represents a type of market incompleteness. Our main focus is on how the presence of the multiplicative background risk y\~ affects risk-taking behavior for decisions on the choice of x\~. We extend the results of Gollier and Pratt (1996) to characterize conditions on preferences that lead to more cautious behavior.

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File URL: http://dx.doi.org/10.1287/mnsc.1050.0450
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Article provided by INFORMS in its journal Management Science.

Volume (Year): 52 (2006)
Issue (Month): 1 (January)
Pages: 146-153

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Handle: RePEc:inm:ormnsc:v:52:y:2006:i:1:p:146-153
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  1. 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.
  2. Jens Carsten Jackwerth, 1998. "Recovering Risk Aversion from Option Prices and Realized Returns," Finance 9803002, EconWPA.
  3. Ogaki, Masao & Zhang, Qiang, 2001. "Decreasing Relative Risk Aversion and Tests of Risk Sharing," Econometrica, Econometric Society, vol. 69(2), pages 515-26, March.
  4. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
  5. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  6. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
  7. Stephen A. Ross, 2004. "Compensation, Incentives, and the Duality of Risk Aversion and Riskiness," Journal of Finance, American Finance Association, vol. 59(1), pages 207-225, 02.
  8. 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.
  9. Guiso, Luigi & Jappelli, Tullio & Terlizzese, Daniele, 1996. "Income Risk, Borrowing Constraints, and Portfolio Choice," American Economic Review, American Economic Association, vol. 86(1), pages 158-72, March.
  10. Donald Meyer & Jack Meyer, 2005. "Relative Risk Aversion: What Do We Know?," Journal of Risk and Uncertainty, Springer, vol. 31(3), pages 243-262, December.
  11. 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.
  12. 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.
  13. Kihlstrom, Richard E & Romer, David & Williams, Steve, 1981. "Risk Aversion with Random Initial Wealth," Econometrica, Econometric Society, vol. 49(4), pages 911-20, June.
  14. 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.
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