By Lars Tyge Nielsen
Scandinavian Journal of Economics 87 (1985), 463-473.
A compound of many independent replicas of an investment or gamble may be attractive to some risk-averters who do not accept the individual investment or gamble. This can happen if there is a chance that the compound leads to a wealth level where the degree of risk aversion is lower than at the initial wealth level. It can also happen if the investor has some sort of limited liability. The von Neumann-Morgenstern utility functions with the property that sufficiently long sequences of repetitions of any fair gamble are preferred to all finite wealth levels are characterized in this paper.