Skip to main content

The Effects of Changes in Risk on Risk Taking: A Survey

  • Chapter

Abstract

We examine an important class of decision problems under uncertainty that entails the standard portfolio problem and the demand for coinsurance. The agent faces a controllable risk—his demand for a risky asset for example—and a background risk. We determine how a change in the distribution in one of these two risks affects the optimal exposure to the controllable risk. Restrictions on first order and second order stochastic dominance orders are in general necessary to yield an unambiguous comparative statics property. We also review another line of research in which restrictions are made on preferences rather than on stochastic dominance orders.

We thank two referees for their useful comments on a preliminary version of the chapter.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Alarie, Y., G. Dionne and L. Eeckhoudt (1992). “Increases in Risk and the Demand for Insurance,” in Contributions to Insurance Economics, Dionne Georges, ed., Kluwer Academic Press, Boston.

    Google Scholar 

  • Athey, S. (1997). “Comparative Statics Under Uncertainty: Single Crossing Properties and Log supermodularity,” mimeo, MIT.

    Google Scholar 

  • Black, J. and G. Bulkley (1989). “A Ratio Criterion for Signing the Effects of an Increase in Uncertainty,” International Economic Review, 30, 119–130.

    Article  Google Scholar 

  • Cheng, H.C., M. Magill and W. Shafer (1987). “Some Results on Comparative Statics under Uncertainty,” International Economic Review, 28, 493–507.

    Article  Google Scholar 

  • Dionne, G., L. Eeckhoudt and C. Gollier (1993). “Increases in Risk and Linear Payoffs,” International Economic Review, 34, 309–319.

    Article  Google Scholar 

  • Dionne, G. and E Gagnon (1996). “Increases in Risk and Optimal Portfolio,” mimeo, Université de Montréal.

    Google Scholar 

  • Dionne, G. and C. Gollier (1992). “Comparative Statics under Multiple Sources of Risk with Applications to Insurance Demand,” The Geneva Papers on Risk and Insurance Theory, 17, 21–33.

    Article  Google Scholar 

  • Dionne, G. and C. Gollier (1996). “A Model of Comparative Statics for Changes in Stochastic Returns with Dependent Risky Assets,” Journal of Risk and Uncertainty, 13, 147–162.

    Article  Google Scholar 

  • Doherty, N. and H. Schlesinger (1983). “Optimal Insurance in Incomplete Markets,” Journal of Political Economy, 91, 1045–1054.

    Article  Google Scholar 

  • Eecckhoudt, L. and M.S. Kimball (1992). “Background Risk, Prudence, and the Demand for Insurance,” in Contributions to Insurance Economics, Dionne Georges, ed., Kluwer Academic Press, Boston.

    Google Scholar 

  • Eeckhoudt, L., C. Gollier and M. Levasseur (1994). “The Economics of Adding and Subdividing Independent Risks: Some Comparative Statics Results,” Journal of Risk and Uncertainty, 8, 325–337.

    Google Scholar 

  • Eeckhoudt, L. and C. Gollier (1995). Risk: Evaluation, Management and Sharing, Hearvester Wheatsheaf, 347 pages.

    Google Scholar 

  • Fishburn, P. and B. Porter (1976). “Optimal Portfolios with One Safe and One Risky Asset: Effects of Changes in Rate of Return and Risk,” Mangement Science, 22, 1064–1073.

    Article  Google Scholar 

  • Gollier, C. (1995). “The Comparative Statics of Changes in Risk Revisited,” Journal of Economic Theory, 66, 522–536.

    Article  Google Scholar 

  • Gollier, C. (1997). “A Note on Portfolio Dominance,” Review of Economic Studies, 64, 147–150.

    Article  Google Scholar 

  • Gollier, C. and M.S. Kimball (1997). “Toward a systematic approach to the economic effects of uncertainty: Characterizing untility functions,” Discussion paper, U. of Michigan.

    Google Scholar 

  • Gollier, C., J. Lindsey and R.J. Zeckhauser (1997). “Investment Flexibility and the Acceptance of Risk,” Journal of Economic Theory, forthcoming.

    Google Scholar 

  • Gollier, C. and J.W. Pratt (1996). “Risk Vulnerability and the Tempering Effect of Background Risk,” Econometrica, 64, 1109–1123.

    Article  Google Scholar 

  • Gollier, C. and P. Scarmure (1994). “The Spillover Effect of Compulsory Insurance, The Geneva Papers on Risk and Insurance Theory,” 19, 23–34.

    Article  Google Scholar 

  • Gollier, C. and E.E. Schlee (1997). “Increased Risk Taking with Multiple Risks,” mimeo, University of Toulouse.

    Google Scholar 

  • Gollier, C. and H. Schlesinger (1996). “Portfolio Choice Under Noisy Asset Returns,” Economics Letters, 53, 47–51.

    Article  Google Scholar 

  • Hadar, J. and W. Russell (1969). “Rules for Ordering Uncertain Prospects,” American Economic Review, 59, 25–34.

    Google Scholar 

  • Hadar, J. and T.K. Seo (1990). “The Effects of Shifts in a Return Distribution on Optimal Portfolios,” International Economic Review, 31, 721–736.

    Article  Google Scholar 

  • Hardy, G.H., J.E. Littlewood and G. Polya (1929). “Some Simple Inequalities Satisfied by Convex Functions,” Messenger of Mathematics, 58, 145–152.

    Google Scholar 

  • Kihlstrom, R., D. Romer and S. Williams (1981). “Risk Aversion with Random Initial Wealth,” Econometrica, 49, 911–920.

    Article  Google Scholar 

  • Landsberger, M. and I. Meilijson (1990). “Demand for Risky Financial Assets: A Portfolio Analysis,” Journal of Economic Theory, 12, 380–391.

    Google Scholar 

  • Levy, H. (1992). “Stochastic Dominance and Expected Utility: Survey and Analysis,” Management Sciences, 38, 555–593.

    Article  Google Scholar 

  • Meyer, D.J. and J. Meyer (1998). “Changes in Background Risk and the Demand for Insurance,” The Geneva Papers on Risk and Insurance Theory, 23, 29–40.

    Article  Google Scholar 

  • Meyer, J. and M. Ormiston (1985). “Strong Increases in Risk and their Comparative Statics,” International Economic Review, 26, 425–437.

    Article  Google Scholar 

  • Meyer, J. and M. Ormiston (1989). “Deterministic Tranformation of Random Variables and the Comparative Statics of Risk,” Journal of Risk and Uncertainty, 2, 179–188.

    Article  Google Scholar 

  • Milgrom, P. (1981). “Good News and Bad News: Representation Theorems and Application,” Bell Journal of Economics, 12, 380–391.

    Article  Google Scholar 

  • Ormistion, M.B. and E.E. Schlee (1993). “Comparative Statics under Uncertainty for a Class of Economic Agents,” Journal of Economic Theory, 61, 412–422.

    Article  Google Scholar 

  • Pratt, J. (1964). “Risk Aversion in the Small and in the Large,” Econometrica, 32, 122–136.

    Article  Google Scholar 

  • Rothschild, M. and J. Stiglitz (1970). “Increasing Risk: I. A Definition,” Journal of Economic Theory, 2, 225–243.

    Article  Google Scholar 

  • Rothschild, M. and J. Stiglitz (1971). “Increasing Risk: II Its Economic Consequences,” Journal of Economic Theory, 3, 66–84.

    Article  Google Scholar 

  • Sandmo, A. (1971). “On the Theory of the Competitive Firm Under Price Uncertainty,” American Economic Review, 61, 65–73.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media New York

About this chapter

Cite this chapter

Eeckhoudt, L., Gollier, C. (2000). The Effects of Changes in Risk on Risk Taking: A Survey. In: Dionne, G. (eds) Handbook of Insurance. Huebner International Series on Risk, Insurance, and Economic Security, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0642-2_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-0642-2_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-7911-9

  • Online ISBN: 978-94-010-0642-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics