### Abstract

We 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, {Mathematical expression} where v(·) 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). We study (i) the properties of the RCE, (ii) the recoverability of v(·) from S_{v}(·) (in terms of the rate of change in risk), (iii) comparison with the "classical CE"u^{-1}Eu(·) 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.

Original language | English (US) |
---|---|

Pages (from-to) | 1-44 |

Number of pages | 44 |

Journal | Annals of Operations Research |

Volume | 30 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 1991 |

### All Science Journal Classification (ASJC) codes

- Decision Sciences(all)
- Management Science and Operations Research

### Keywords

- Stochastic optimization with recourse
- certainty equivalents
- decision-making under uncertainty
- expected utility
- insurance
- investment in risky and safe assets
- production under price uncertainty
- risk aversion
- the Allais paradox and other decision theoretic paradoxes

## Fingerprint Dive into the research topics of 'A recourse certainty equivalent for decisions under uncertainty'. Together they form a unique fingerprint.

## Cite this

*Annals of Operations Research*,

*30*(1), 1-44. https://doi.org/10.1007/BF02204807