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Multiplicative Background Risk

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Author Info

  • Günter Franke

    ()
    (Department of Economics, University of Konstanz)

  • Harris Schlesinger

    ()
    (University of Alabama)

  • Richard C. Stapleton

    ()
    (University of Manchester and University of Melbourne)

Abstract

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 xy, 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, which 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 characterize conditions on preferences that lead to more cautious behavior.

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Bibliographic Info

Paper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 03-05.

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Length: 33 pages
Date of creation: May 2003
Date of revision:
Handle: RePEc:knz:cofedp:0305

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Related research

Keywords: multiplicative risks; background risk; incomplete markets; standard risk aversion; affiliated utility function; multiplicative risk vulnerability;

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References

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  1. Kihlstrom, Richard E & Romer, David & Williams, Steve, 1981. "Risk Aversion with Random Initial Wealth," Econometrica, Econometric Society, vol. 49(4), pages 911-20, June.
  2. 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.
  3. Guiso, Luigi & Jappelli, Tullio & Terlizzese, Daniele, 1994. "Income Risk, Borrowing Constraints and Portfolio Choice," CEPR Discussion Papers 888, C.E.P.R. Discussion Papers.
  4. Christian Gollier, 2004. "The Economics of Risk and Time," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262572249, December.
  5. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
  6. Masao Ogaki & Qiang Zhang, 1998. "Decreasing Relative Risk Aversion and Tests of Risk Sharing," Working Papers 98-02, Ohio State University, Department of Economics.
  7. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  8. Diamond, Peter A. & Stiglitz, Joseph E., 1974. "Increases in risk and in risk aversion," Journal of Economic Theory, Elsevier, vol. 8(3), pages 337-360, July.
  9. 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.
  10. Jens Carsten Jackwerth, 1998. "Recovering Risk Aversion from Option Prices and Realized Returns," Finance 9803002, EconWPA.
  11. Nachman, David C., 1982. "Preservation of "more risk averse" under expectations," Journal of Economic Theory, Elsevier, vol. 28(2), pages 361-368, December.
  12. Yacine Ait-Sahalia & Andrew W. Lo, 2000. "Nonparametric Risk Management and Implied Risk Aversion," NBER Working Papers 6130, National Bureau of Economic Research, Inc.
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