A von Neumann–Morgenstern Representation Result without Weak Continuity Assumption
Please always quote using this URN:urn:nbn:de:0296-matheon-9990
- In the paradigm of VON N EUMANN AND M ORGENSTERN, a representation of affine pref- erences in terms of an expected utility can be obtained under the assumption of weak continu- ity. Since the weak topology is coarse, this requirement is a priori far from being negligible. In this work, we replace the assumption of weak continuity by monotonicity. More precisely, on the space of lotteries on an interval of the real line, it is shown that any affine preference order which is monotone with respect to the first stochastic order admits a representation in terms of an expected utility for some nondecreasing utility function. As a consequence, any affine preference order on the subset of lotteries with compact support, which is monotone with respect to the second stochastic order, can be represented in terms of an expected util- ity for some nondecreasing concave utility function. We also provide such representations for affine preference orders on the subset of those lotteries which fulfill some integrability conditions. The subtleties of the weak topology are illustrated by some examples.
Author: | Freddy Delbaen, Samuel Drapeau, Michael Kupper |
---|---|
URN: | urn:nbn:de:0296-matheon-9990 |
Referee: | Dirk Becherer |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2012/01/27 |
Release Date: | 2012/01/27 |
Institute: | Humboldt-Universität zu Berlin |
MSC-Classification: | 91-XX GAME THEORY, ECONOMICS, SOCIAL AND BEHAVIORAL SCIENCES / 91Bxx Mathematical economics (For econometrics, see 62P20) / 91B06 Decision theory [See also 62Cxx, 90B50, 91A35] |
Preprint Number: | 889 |