RT Journal Article
T1 Maxentropic Solutions to a Convex Interpolation Problem Motivated by Utility Theory
A1 Gzyl Buchholz, Henryk
A1 Mayoral, Silvia
AB 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)dFXi(x)=πi where the Xi are random variables taking values on [a,b] and πi 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 Xi 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.
PB MDPI
SN 1099-4300
YR 2017
FD 2017-04-01
LK https://hdl.handle.net/10016/27887
UL https://hdl.handle.net/10016/27887
LA eng
NO All sources of funding of the study should be disclosed. Please clearly indicate grants that you have received in support of your research work. Clearly state if you received funds for covering the costs to publish in open access.
DS e-Archivo
RD 28 may. 2024