Bell poses and explores an interesting issue in decision  theory:  under what specifications of a utility (of wealth) function is it always advantageous to resolve larger rather than smaller uncertainties regarding one’s wealth before making a risky decision? Intuitively, it would seem that resolving the larger uncertainty is always preferable to resolving the smaller one (assuming only one can be resolved). Bell shows, however, that there is only one specification of a utility of wealth function that both satisfies the usual restrictions on such functions (that they be strictly increasing functions of wealth and exhibit risk aversion) and shows that a decision maker is always better off resolving the larger uncertainty (at all levels of wealth). That utility function is the linear plus exponential form U ( W ) = a W - b e ^{- c W}, where U ( W ) is the utility index for wealth, W is the measure of wealth, e is the base of the natural logarithms, and parameters a, b, and c are greater than or equal to 0. The paper provides both an intuitive explanation and a mathematical proof of the proposition. In concluding, the author suggests that this function deserves consideration as the utility function for generic analyses of financial risk taking.

Because the function approaches risk neutrality (linearity) as wealth gets arbitrarily large, it may not be quite so intuitively appealing or universally appropriate as the author suggests. Indeed, in casual exploration of the function, I found it difficult to model significant diminishing marginal utility over a broad range of wealth.

Nonetheless, modelers of decision processes and developers of decision aids will find this paper both interesting and useful.