ABSTRACT
The importance of risk and uncertainty in economic analysis was suggested for the first time by Frank H. Knight in his seminal treatise Risk, Uncertainty and Profit (see [328]). Previously, very few economists considered that risk and uncertainty might play a key role in economic theory, except for some notable examples like Carl Menger [384], Irving Fisher [227] and Francis Edgeworth [186]. The problem was:
• First, to define precisely the notions of “uncertainty” or “risk” when events are random; and,
• Second, to model the choice process within risk and uncertainty. The notion of choice under risk and uncertainty was not well modelled for a long time, despite the results of Hicks [293] and Marschak [377], who understood that preferences should be defined also on distributions, to take account simultaneously of the evaluation of the level of risk or uncertainty, and of the pure preferences over outcomes. However, Bernoulli [54] had formerly introduced the notion of expected utility to solve the famous St.Petersburg paradox posed in 1713. The expected utility theory allows the representation of the level of satisfaction by the sum of utilities from outcomes weighted by the probabilities of these outcomes. Nevertheless, in that case, a gain can increase utility less than a decline can reduce it, which was not considered as rational.
