A recourse certainty equivalent for decisions under uncertainty

We propose a new criterion fordecision-making under uncertainty. The criterion is based on acertainty equivalent (CE) of a (monetary valued) random variable Z, $$S_\upsilon (Z) = \mathop {\sup }\limits_z \{ z + E_Z \upsilon (Z - z)\} ,$$ wherev(·) is the decision maker'svalue-risk function. This CE is derived from considerations ofstochastic optimization with recourse, and is calledrecourse certainty equivalent (RCE). We study (i) the properties of the RCE, (ii) the recoverability ofv(·) fromS _v (·) (in terms of the rate of change in risk), (iii) comparison with the “classical CE”u ^?1 Eu(·) inexpected utility (EU) theory, (iv) relation to risk-aversion, (v) connection with Machina'sgeneralized expected utility theory, and its use to explain theAllais paradox and other decision theoretic paradoxes, and (vi) applications to models ofproduction under price uncertainty, investment in risky and safe assets andinsurance. In these models the RCE gives intuitively appealing answers forall 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-calledArrow-Pratt indices.