Skip to main content

Relationships Between Archimedean Copulas and Morgenstern Utility Functions

Part of the Lecture Notes in Statistics book series (LNSP,volume 198)

Abstract

The (additive) generator of an Archimedean copula is a strictly decreasing and convex function, while Morgenstern utility functions (applying to risk aversion decision makers) are nondecreasing and concave. In this presentation, relationships between generators and utility functions are established. For some well known Archimedean copula families, links between the generator and the corresponding utility function are demonstrated. Some new copula families are derived from classes of utility functions which appeared in the literature, and their properties are discussed. It is shown how dependence properties of an Archimedean copula translate into properties of the utility function from which they are constructed.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-642-12465-5_17
  • Chapter length: 12 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   149.00
Price excludes VAT (USA)
  • ISBN: 978-3-642-12465-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   199.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arrow, K.J.: Essays in the Theory of Risk Bearing. Chicago: Markham Publishing (1971).

    Google Scholar 

  2. Avérous, J., and Dortet-Bernadet, J.-L.: Dependence for Archimedean copulas and aging properties of their generating functions. Sankhy¯a: The Indian Journal of Statistics, 66 (4), 1-14 (2004).

    Google Scholar 

  3. Esary, J.D. and Proschan, F.: Relationships among some concepts of bivariate dependence. Annals of Mathematical Statistics 43 (2), 651-655 (1972).

    MATH  CrossRef  MathSciNet  Google Scholar 

  4. Genest, C., Ghoudi, K. & Rivest L.-P.: A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika 82, 543-552 (1995).

    MATH  CrossRef  MathSciNet  Google Scholar 

  5. Hougaard, P.: Analysis of Multivariate Survival Data. Springer (2000).

    Google Scholar 

  6. Lehmann, E.L.: Some concepts of dependence. Annals of Mathematical Statistics 37, 1137-1153 (1966).

    MATH  CrossRef  MathSciNet  Google Scholar 

  7. Merton, R.C.: Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory (3), 373-413 (1971). 322 Jaap Spreeuw

    Google Scholar 

  8. Nelsen, R.B.: An Introduction to Copulas. Springer, Second Edition (2006).

    Google Scholar 

  9. Pratt, J.W.: Risk aversion in the small and in the large. Econometrica 32 (1-2), 122-136 (1964).

    MATH  CrossRef  Google Scholar 

  10. Saha, A.: Expo-power utility: a flexible form for absolute and relative risk aversion. American Journal of Agricultural Economics 75, 905-913 (1993).

    CrossRef  Google Scholar 

  11. Spreeuw, J.: Types of dependence and time-dependent association between two lifetimes in single parameter copula models. Scandinavian Actuarial Journal 2006 (5), 286-309 (2006).

    MATH  CrossRef  MathSciNet  Google Scholar 

  12. Xie, D.: Power risk aversion utility functions. Annals of Economics and Finance 1, 265-282 (2000).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jaap Spreeuw .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2010 Springer Berlin Heidelberg

About this paper

Cite this paper

Spreeuw, J. (2010). Relationships Between Archimedean Copulas and Morgenstern Utility Functions. In: Jaworski, P., Durante, F., Härdle, W., Rychlik, T. (eds) Copula Theory and Its Applications. Lecture Notes in Statistics(), vol 198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12465-5_17

Download citation