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Maxentropic Solutions to a Convex Interpolation Problem Motivated by Utility Theory

by Henryk Gzyl 1,*,† and Silvia Mayoral 2,†
1
Centro de Finanzas, Instituto de Estudios Superiores de Administración (IESA), Caracas 1010, Venezuela
2
Depto de Economía de la Empresa, Charles III University of Madrid (UC3M), Getafe 28903, Spain
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editors: Michael (Mike) Stutzer and Stelios Bekiros
Entropy 2017, 19(4), 153; https://doi.org/10.3390/e19040153
Received: 17 February 2017 / Revised: 21 March 2017 / Accepted: 27 March 2017 / Published: 1 April 2017
(This article belongs to the Special Issue Entropic Applications in Economics and Finance)
Here, we consider the following inverse problem: Determination of an increasing continuous function U ( x ) on an interval [ a , b ] from the knowledge of the integrals U ( x ) d F X i ( x ) = π i where the X i are random variables taking values on [ a , b ] and π i are given numbers. This is a linear integral equation with discrete data, which can be transformed into a generalized moment problem when U ( x ) is supposed to have a positive derivative, and it becomes a classical interpolation problem if the X i are deterministic. In some cases, e.g., in utility theory in economics, natural growth and convexity constraints are required on the function, which makes the inverse problem more interesting. Not only that, the data may be provided in intervals and/or measured up to an additive error. It is the purpose of this work to show how the standard method of maximum entropy, as well as the method of maximum entropy in the mean, provides an efficient method to deal with these problems. View Full-Text
Keywords: inverse problems; interpolation problems; uncertain data; maximum entropy; utility function inverse problems; interpolation problems; uncertain data; maximum entropy; utility function
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Gzyl, H.; Mayoral, S. Maxentropic Solutions to a Convex Interpolation Problem Motivated by Utility Theory. Entropy 2017, 19, 153.

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