Prudence and preference for flexibility gain

We investigate the properties of the preference of an individual for an unknown profit pi(x) over a certain profit pi(E(x)), where x is unknown at the time when the decision is made, whereas its expected value E(x) is known. The additional benefit to the individual of the former over the latter consists in a flexibility gain. For instance, a flexibility gain arises in investment decisions when the individual obtains a higher benefit if she postpones the investment until after some technology x is realized, rather than making it today with technology E(x). We show that prudence (positive third derivative of the utility function) is related to the size of the flexibility gain, in the same vein as it is related to the utility premium of an individual who prefers a certain profit p to a variable profit pi + ??, where E(??) = 0. We further examine the way in which the concept of flexibility gain is linked to a variety of notions and problems, namely downside risk aversion, concave surplus of a risk neutral individual, stochastic dominance, optimal prevention, and principal-agent relationships with unknown distribution of some relevant variable. This permits to highlight the role of the degree of absolute prudence (or of the third derivative of the surplus function, when the individual is risk neutral) in decision making.