Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T07:10:40.790Z Has data issue: false hasContentIssue false
  • English
  • Français

When Many Wrongs Make a Right

An Asymptotic Analysis of Risk Aversion and Additive Risks

Published online by Cambridge University Press:  27 July 2009

Steven A. Lippman  and
John W. Mamer
Steven A. Lippman
Affiliation:
University of California, Los Angeles Los Angeles, California 90024
John W. Mamer
Affiliation:
University of California, Los Angeles Los Angeles, California 90024
Get access Rights & Permissions [Opens in a new window]

Abstract

When confronted by a sequence of independent, identical, favorable-though- risky investments, a risk-averse agent will in fact elect to invest as part of a large syndicate even if he or she would not undertake even one of the investments by himself or herself. This willingness to invest emanates from the risk reduction associated with the risk pooling effected by the syndicate. Our first two theorems describe the syndicate size needed to induce the agent's participation.

The consequence of adding risks is considered next. We demonstrate that the agent will undertake a large number of these independent investments by himself or herself even if each investment taken by itself constitutes a poor risk. The conditions needed to ensure this somewhat surprising result are (a) moment bounds on the investments, and (b) either a polynomial or an exponential bound on the lower tail of the agent's utility function. Finally, we draw the connection between this result, proper risk aversion, and monotonicity of the agent's absolute aversion to risk.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 1 , January 1988 , pp. 115 - 127
Copyright
Copyright © Cambridge University Press 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arrow, K.J. (1971). Essays in the theory of risk bearing. Amsterdam: North-Holland.Google Scholar
Chung, K.L. (1968). A course in probability theory. New York: Harcourt, Brace.Google Scholar
Diamond, D.W. (1984). Financial intermediation and delegated monitoring. Review of Economic Studies 51: 393–414.Google Scholar
Feller, W. (1966). An introduction to probability theory and its applications, vol. II. New York:John Wiley & Sons, Inc.Google Scholar
Kihlstrom, R.E., Romer, D. & Williams, S. (1981). Risk aversion with random initial wealth. Econometrica 49: 911–920.CrossRefGoogle Scholar
Nielsen, L.T. (1985). Attractive compounds of unattractive investments and gambles. Scandinavian Journal of Economics 87: 463–473.Google Scholar
Pratt, J.W. & Zeckhauser, R.J. (1987). Proper risk aversion. Econometrica 55: 143–154.CrossRefGoogle Scholar
Samuelson, P.A. (05 1984). Additive insurance via the N law: Domar–Musgrave to the rescue of the Brownian motive. Unpublished manuscript.Google Scholar