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Multiplicative Background Risk

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Author Info

  • 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)

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 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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Bibliographic Info

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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Related research

Keywords: affiliated utility function; background risk; diffidence theorem; multiplicative risks; multiplicative risk vulnerability; risk vulnerability;

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References

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  1. Masao Ogaki & Qiang Zhang, 1998. "Decreasing Relative Risk Aversion and Tests of Risk Sharing," Working Papers 98-02, Ohio State University, Department of Economics.
  2. 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.
  3. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  4. Nachman, David C., 1982. "Preservation of "more risk averse" under expectations," Journal of Economic Theory, Elsevier, vol. 28(2), pages 361-368, December.
  5. Christian Gollier, 2004. "The Economics of Risk and Time," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262572249, January.
  6. Jens Carsten Jackwerth., 1996. "Recovering Risk Aversion from Option Prices and Realized Returns," Research Program in Finance Working Papers RPF-265, University of California at Berkeley.
  7. 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.
  8. Guiso, Luigi & Jappelli, Tullio & Terlizzese, Daniele, 1994. "Income Risk, Borrowing Constraints and Portfolio Choice," CEPR Discussion Papers 888, C.E.P.R. Discussion Papers.
  9. 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.
  10. Miles S. Kimball, 1991. "Standard Risk Aversion," NBER Technical Working Papers 0099, National Bureau of Economic Research, Inc.
  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. Kihlstrom, Richard E & Romer, David & Williams, Steve, 1981. "Risk Aversion with Random Initial Wealth," Econometrica, Econometric Society, vol. 49(4), pages 911-20, June.
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Citations

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Cited by:
  1. Malevergne, Y. & Rey, B., 2009. "On cross-risk vulnerability," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 224-229, October.
  2. Franke, Guenter & Schlesinger, Harris & Stapleton, Richard C., 2011. "Risk taking with additive and multiplicative background risks," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1547-1568, July.
  3. Guo, Xu & Wong, Wing-Keung & Zhu, Lixing, 2013. "An analysis of portfolio selection with multiplicative background risk," MPRA Paper 51331, University Library of Munich, Germany.
  4. Guenter Franke & Harris Schlesinger & Richard C. Stapleton, 2013. "Risk-Taking-Neutral Background Risk," CESifo Working Paper Series 4070, CESifo Group Munich.
  5. Jiang, Chonghui & Ma, Yongkai & An, Yunbi, 2010. "An analysis of portfolio selection with background risk," Journal of Banking & Finance, Elsevier, vol. 34(12), pages 3055-3060, December.
  6. Nicos Scordis, 2011. "The Morality of Risk Modeling," Journal of Business Ethics, Springer, vol. 103(1), pages 7-16, April.
  7. Broll, Udo & Wong, Keith K.P., 2010. "The firm under uncertainty: capital structure and background risk," Dresden Discussion Paper Series in Economics 04/10, Dresden University of Technology, Faculty of Business and Economics, Department of Economics.
  8. EECKHOUDT, Louis & ETNER, Johanna & SCHROYEN, Fred, . "The values of relative risk aversion and prudence: A context-free interpretation," CORE Discussion Papers RP -2162, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Alghalith, Moawia, 2012. "The impact of background risk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6506-6508.
  10. Moawia Alghalith, 2008. "Hedging and production decisions under uncertainty: A survey," Papers 0810.0917, arXiv.org.
  11. Jokung, Octave, 2011. "Risk apportionment via bivariate stochastic dominance," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 448-452.
  12. Jiang, Chonghui & Ma, Yongkai & An, Yunbi, 2013. "International portfolio selection with exchange rate risk: A behavioural portfolio theory perspective," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 648-659.
  13. Alexandru V. Asimit & Raluca Vernic & Riċardas Zitikis, 2013. "Evaluating Risk Measures and Capital Allocations Based on Multi-Losses Driven by a Heavy-Tailed Background Risk: The Multivariate Pareto-II Model," Risks, MDPI, Open Access Journal, vol. 1(1), pages 14-33, March.
  14. Chiaki Hara & James Huang & Christoph Kuzmics, 2006. "Efficient Risk-Sharing Rules with Heterogeneous Risk Attitudes and Background Risks," KIER Working Papers 621, Kyoto University, Institute of Economic Research.
  15. Udo Broll & Kit Wong, 2013. "The firm under uncertainty: real and financial decisions," Decisions in Economics and Finance, Springer, vol. 36(2), pages 125-136, November.
  16. Louis Eeckhoudt & Béatrice Rey, 2011. "Risk vulnerability: a graphical interpretation," Theory and Decision, Springer, vol. 71(2), pages 227-234, August.
  17. Georges Dionne & Jingyuan Li, 2012. "Comparative Ross Risk Aversion in the Presence of Quadrant Dependent Risks," Cahiers de recherche 1226, CIRPEE.
  18. Lionel, ARTIGE, 2004. "Optimal Saving with Additive and Multiplicative Background Risk," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2004030, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  19. Huang, Hung-Hsi & Wang, Ching-Ping, 2013. "Portfolio selection and portfolio frontier with background risk," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 177-196.
  20. Adam-Müller, Axel F.A. & Nolte, Ingmar, 2011. "Cross hedging under multiplicative basis risk," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 2956-2964, November.
  21. Georges Dionne & Jingyuan Li, 2012. "Comparative Ross Risk Aversion in the Presence of Mean Dependent Risks," Cahiers de recherche 1211, CIRPEE.

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