The assessment of large compounds of independent gambles

The paper gives necessary and sufficient conditions for an expected-utility-maximizing decision maker to prefer any compound Sigma(i)(n)=1 <(X)over tilde(i)> of n independent, identically distributed random variables over any other such compound Sigma(i)(n)=1 <(Y)over tilde(i)> with E<(Y)over tilde(i)> < E<(X)over tilde(i)>, provided that n is sufficiently large. A sufficient condition is that absolute risk aversion go to zero as the decision maker's wealth becomes unboundedly positive or negative. The analysis is applied to give necessary and sufficient conditions for the desirability of ''max-expected-log'' policies in multiperiod choice problems with a distant time horizon. (C) 1995 Academic Press, Inc.