Skip to main content
Log in

Multivariate risk premiums

  • Published:
Theory and Decision Aims and scope Submit manuscript

Abstract

This paper develops characterizations of a risk premium and of the relation “more risk averse”, for multi-dimensional problems where the agent is exposed to an insurable and an uninsurable risk. We generalize and inter-relate results of Duncan (1977), Karni (1979), Kihlstrom et al. (1981), Malinvaud (1971), and Ross (1981) in deriving a local ordering of the risk aversion of agents with differing ordinal preferences.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ambarish, R. and Kallberg, J. G.: 1983, ‘Risk Aversion and Minimum Concave Utility Functions’, New York University, Working Paper.

  • Arrow, K. J.: 1971, Essays in the Theory of Risk-Bearing, Markham, New York.

    Google Scholar 

  • Bellman, R.: 1959, Introduction to Matrix Analysis, McGraw-Hill, New York.

    Google Scholar 

  • Caperaa, P. and Eeckhoudt, L.: 1976, ‘Delayed Risks and Risk Premiums’, JFE, 2.

  • Dempster, A. P.: 1969, Elements of Continuous Multivariate Analysis, Addison-Wesley, Reading.

    Google Scholar 

  • Dreze, J. H. and Modigliani, F.: 1972, ‘Consumption Decisions under Uncertainty’, JET, 5.

  • Duncan, G. T.: 1977, ‘A Matrix Measure of Multivariate Local Risk Aversion’, Econometrica 45.

  • Hille, E.: 1959, Analytic Function Theory, Vol. 1, Blaisdell, New York.

    Google Scholar 

  • Kallberg, J. G. and Ziemba, W. T.: 1983, ‘A Comparison of Alternative Utility Functions in Portfolio Theory’, Management Science 29.

  • Karni, E.: 1979, ‘On Multivariate Risk Aversion’, Econometrica 47.

  • Kihlstrom, R. E. and Mirman, L. J.: 1974, ‘On Risk Aversion with Many Commodities’, JET, 8.

  • Kihlstrom, R. E. and Mirman, L. J.: 1981, ‘Constant, Increasing, and Decreasing Risk Aversion with Many Commodities’, R.E. Studies 48.

  • Kihlstrom, R. E., Romer, D. and Williams, S.: 1981, ‘Risk Aversion with Random Initial Wealth’, Econometrica 49.

  • Kreps, D. M. and Porteus, E. L.: 1978, ‘Temporal Resolution of Uncertainty and Dynamic Choice Theory’, Econometrica 46.

  • Malinvaud, E.: 1971, Lectures on Microeconomic Theory, North-Holland, Amsterdam.

    Google Scholar 

  • Nachman, D. C.: 1975, ‘Risk Aversion, Impatience, and Optimal Timing Decisions’, JET 11.

  • Paroush, J.: 1975, ‘Risk Premiums with Many Commodities’, JET 11.

  • Pratt, J.: 1964, ‘Risk Aversion in the Small and in the Large’, Econometrica 32.

  • Rao, C. R. and Mitra, S. K.: 1971, Generalized Inverse of Matrices and Its Applications, Wiley, New York.

    Google Scholar 

  • Ross, S. A.: 1981, ‘Some Stronger Measures of Risk Aversion in the Small and in the Large with Applications’, Econometrica 49.

  • Rubinstein, M. E.: 1973, ‘The Fundamental Theorem of Parameter Preference in Security Valuation’, JFQA 8.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Earlier versions of this paper have been presented at seminars at New York University, the University of Alberta, and the University of British Columbia. We would like to acknowledge the helpful comments of participants at these presentations, in particular, Yakov Amihud, David Nachman, Joel Owen, Siegfried Schaible, Gordon Sick, and William Ziemba. All responsibility for errors and omissions resides with the authors.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ambarish, R., Kallberg, J.G. Multivariate risk premiums. Theor Decis 22, 77–96 (1987). https://doi.org/10.1007/BF00125658

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00125658

Keywords

Navigation