The authors propose a new criterion for decision-making under uncertainty. The criterion is based on a certainty equivalent (CE) of a (monetary valued) random variable Z, 
, where 
is the decision maker's value-risk function. This CE is derived from considerations of stochastic optimization with recourse, and is called recourse certainty equivalent (RCE). The authors study (i) the properties of the RCE, (ii) the recoverability of 
from 
(in terms of the rate of change in risk), (iii) comparison with the ‘classical CE’ 
in expected utility (EU) theory, (iv) relation to risk-aversion, (v) connection with Machina's generalized expected utility theory, and its use to explain the Allais paradox and other decision theoretic paradoxes, and (vi) applications to models of production under price uncertainty, investment in risky and safe assets and insurance. In these models the RCE gives intuitively appealing answers for all risk-averse decision makers, unlike the EU model which gives only partial answers, and requires, in addition to risk-aversion, also assumptions on the so-called Arrow-Pratt indices.
