Title: Using Soft Data to Make "Probabilisitc Risk Assessments" Realistic, Rex Brown
Authors: Rex Brown, George Mason University
Date: April 1999
Status: working paper
 

The risk premium of a gamble, first derived independently by Arrow and Pratt, depends upon three characteristics, the form of the utility function, the distribution of the gamble considered (and so the distribution of final wealth) and the level of initial wealth.  Several studies have analysed what desirable features of these for a 'sensible' financial investor.  Arrow and Pratt themselves argue that the link between the utility function and wealth should be that absolute risk aversion should decrease in wealth while, in some cases, relative risk aversion should increase.  Likewise, Rothschild and Stiglitz provide a characterisation of how changes in distributions affect the risk premium for the class of utility functions which are increasing and concave.  This includes the notion of stochastic dominance, which is one of the most frequently used risk characterisations in finance.  However, the link between final wealth (essentially thorough the choice of distribution on the gamble) and the initial wealth has not, to the authors knowledge, been analysed in the present finance literature.  This paper discusses the motivation for looking at multiplicative gambles and more complicated risk exposures, provides basic results on fundamental expected utility theory under these conditions, identifies the conditions for preference switching for specific utility functions, and addresses risk-return separation. **

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** this abstract was prepared by the editor of the decision analysis working paper archive.

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