Abstract
Risk-aversion is advanced as a measure of the feeling guiding the person who faces a decision with uncertain outcomes, whether about money or status or happiness or anything else of importance. The concepts of utility and, implicitly, risk-aversion were used first nearly 300years ago, but risk-aversion was identified as a key dimensionless variable for explaining monetary decisions only in 1964. A single class of utility function with risk-aversion as sole parameter emerges when risk-aversion is regarded as a function of the present wealth, rather than subject to alteration through imagining possible future wealths. The adoption of a single class allows a more direct analysis of decisions, revealing shortcomings in the use of conventional, Taylor series expansions for inferring risk-aversion, over and above the obvious restrictions on perturbation size. Dimensional analysis shows that risk-aversion is a function of three dimensionless variables particular to the decision and a set of dimensionless character traits, identified later as the limiting reluctance to invest and the lower threshold on risk-aversion. The theoretical framework presented allows measurement of risk-aversion, paving the way for direct, evidence-based utility calculations.
Highlights
Risk-aversion is a fundamental parameter determining how much satisfaction or utility we obtain from an experience, from a good or from money
We could try to reconstruct a decision maker’s utility function from the decisions he takes, by confronting him with a large number of questions like: ‘Which premium P are you willing to pay to avoid a loss . . . that could occur with probability q?’ . . . In practice, we would soon experience the limitations of utility theory: the decision maker will grow increasingly irritated as the interrogation continues and his decisions will become inconsistent”
The paper has reviewed the historical development of the concepts of utility and risk-aversion, starting nearly 300 years ago
Summary
Risk-aversion is a fundamental parameter determining how much satisfaction or utility we obtain from an experience, from a good or from money. The same argument applies to the poor man considering a lottery, and to people of all gradations of wealth in between Nor is it sufficient to have lived in a different state of wealth in the past, since the feelings that the previous condition produced will be remembered so imperfectly that it would not be possible to develop the corresponding level of risk-aversion, even if the person wished so to do. It is expected that the decision maker will vary his risk-aversion during the course of his pondering on his decision, but that risk-aversion will stay constant during each pairwise comparison of the outturn utilities resulting from the adoption or non-adoption of a particular course of action This model is of strong economic importance, since it will be shown that the associated utility functions must be of one class only, namely the Power utility, with risk-aversion as sole parameter. The residual difficulties will be brought out of measuring a parameter that is personal to the individual, and that will vary according to the importance of the decision
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