UPPER BOUNDS OF GENERALIZED ‘USEFUL’ INFORMATION MEASURE WITH APPLICATIONS IN FINANCE
Received: 22.07.2021; Revised: 11.08.2021, Accepted: 16.09.2021, Published Online: 30.09.2021
Pankaj Prasad Dwivedi
Department of Mathematics Jaypee University of Engineering and Technology A.B. Road, Raghogarh, Dist. Guna,473226 India, E-mail address, pankaj.career9@gmail.com
ORCID ID: orcid.org/0000-0002-6873-0910
Dilip Kumar Sharma
Department of Mathematics Jaypee University of Engineering and Technology A.B. Road, Raghogarh, Dist. Guna,473226 India, E-mail address, dilipsharmajiet@gmail.com
ORCID ID: orcid.org/0000-0002-6584-4904
JEL Classification: D63; D81; F31
Keywords: ‘Useful’ Information measure, Expected utility, Generalizations, ‘Useful’ Jensen’s inequality, foreign exchange markets
Abstract
Research background: A measure of the level of uncertainty due to random variables is referred to as “information.” Data measurements have been brought into the literature in the recent decade to solve real-world challenges in finance and economics. In risk analysis and resolving optimization issues under ambiguity, the method based on risk and information measurements provides realistic approaches and efficient computational tools. For dealing with choice issues in the economy, social sciences, and many other disciplines, several mathematical approaches are utilized.
Purpose of the article: Our primary objective for the Classical ‘useful’ information of Shannon is to give a robust upper bound, refining the literature’s recent findings. In the subject of financial economics, the goal of this study is to quantify the extent and statistical importance of inequalities. ‘Useful’ Jensen’s inequality is represented by the given inequalities. It is a comparison of the predicted and actual results.
Methods: The study-focused method of simulation on simulating random normal variables seems to be the approach employed, which introduces sampling error. Regardless of the sampling error, the conclusion is that general disparities are economically significant and statistically significant inequalities. The main conclusion is that, contrary to popular belief, the inequality of Jensen’s is not a conceptual and pointless utilization in economics.
Findings & value-added: Using the approach of simulation of arbitrary standard variables, this article investigated the statistical relevance of variations of Jensen’s inequality applied to banking. In these situations, Jensen’s inequality, when extended to economics, cannot be dismissed as trivial. Furthermore, Jensen’s inequality test ensures that the anticipated utility concept is little more than a theoretical or mathematical activity, but also has statistical backing.