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Econometric applications of maxmin expected utility
Author(s) -
Chamberlain Gary
Publication year - 2000
Publication title -
journal of applied econometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.878
H-Index - 99
eISSN - 1099-1255
pISSN - 0883-7252
DOI - 10.1002/jae.583
Subject(s) - minimax , expected utility hypothesis , axiom , mathematical optimization , mathematics , portfolio , set (abstract data type) , probability distribution , joint probability distribution , prior probability , preference , expected value , decision rule , upper and lower bounds , mathematical economics , portfolio optimization , econometrics , computer science , bayesian probability , statistics , economics , mathematical analysis , geometry , financial economics , programming language
Gilboa and Schmeidler (1989) develop a set of axioms for decision making under uncertainty. The axioms imply a utility function and a set of distributions such that the preference ordering is obtained by calculating expected utility with respect to each distribution in the set, and then taking the minimum of expected utility over the set. In a portfolio choice problem, the distributions are joint distributions for the data that will be available when the choice is made and for the future returns that will determine the value of the portfolio. The set of distributions could be generated by combining a parametric model with a set of prior distributions. We apply this framework to obtain a preference ordering over decision rules, which map the data into a choice. We seek a decision rule that maximizes the minimum expected utility (or, equivalently, minimizes maximum risk) over the set of distributions. An algorithm is provided for the case of a finite set of distributions. It is based on solving a concave programme to find the least‐favourable mixture of these distributions. The minimax rule is a Bayes rule with respect to this least‐favourable distribution. The minimax value is a lower bound for minimax risk relative to a larger set of distributions. An upper bound can be found by fixing a decision rule and calculating its maximum risk. We apply the algorithm to an estimation problem in an autoregressive, random‐effects model for panel data. Copyright © 2000 John Wiley & Sons, Ltd.