Maxentropic Solutions to a Convex Interpolation Problem Motivated by Utility Theory
Centro de Finanzas, Instituto de Estudios Superiores de Administración (IESA), Caracas 1010, Venezuela
Depto de Economía de la Empresa, Charles III University of Madrid (UC3M), Getafe 28903, Spain
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Academic Editors: Michael (Mike) Stutzer and Stelios Bekiros
Received: 17 February 2017 / Revised: 21 March 2017 / Accepted: 27 March 2017 / Published: 1 April 2017
Here, we consider the following inverse problem: Determination of an increasing continuous function
on an interval
from the knowledge of the integrals
are random variables taking values on
are given numbers. This is a linear integral equation with discrete data, which can be transformed into a generalized moment problem when
is supposed to have a positive derivative, and it becomes a classical interpolation problem if the
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.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
Gzyl, H.; Mayoral, S. Maxentropic Solutions to a Convex Interpolation Problem Motivated by Utility Theory. Entropy 2017, 19, 153.
Gzyl H, Mayoral S. Maxentropic Solutions to a Convex Interpolation Problem Motivated by Utility Theory. Entropy. 2017; 19(4):153.
Gzyl, Henryk; Mayoral, Silvia. 2017. "Maxentropic Solutions to a Convex Interpolation Problem Motivated by Utility Theory." Entropy 19, no. 4: 153.
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