Cargando…

Principal Curves for Statistical Divergences and an Application to Finance

This paper proposes a method for the beta pricing model under the consideration of non-Gaussian returns by means of a generalization of the mean-variance model and the use of principal curves to define a divergence model for the optimization of the pricing model. We rely on the q-exponential model s...

Descripción completa

Detalles Bibliográficos
Autores principales: Rodrigues, Ana Flávia P., Cavalcante, Charles Casimiro
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512852/
https://www.ncbi.nlm.nih.gov/pubmed/33265423
http://dx.doi.org/10.3390/e20050333
_version_ 1783586252681904128
author Rodrigues, Ana Flávia P.
Cavalcante, Charles Casimiro
author_facet Rodrigues, Ana Flávia P.
Cavalcante, Charles Casimiro
author_sort Rodrigues, Ana Flávia P.
collection PubMed
description This paper proposes a method for the beta pricing model under the consideration of non-Gaussian returns by means of a generalization of the mean-variance model and the use of principal curves to define a divergence model for the optimization of the pricing model. We rely on the q-exponential model so consider the properties of the divergences which are used to describe the statistical model and fully characterize the behavior of the assets. We derive the minimum divergence portfolio, which generalizes the Markowitz’s (mean-divergence) approach and relying on the information geometrical aspects of the distributions the Capital Asset Pricing Model (CAPM) is then derived under the geometrical characterization of the distributions which model the data, all by the consideration of principal curves approach. We discuss the possibility of integration of our model into an adaptive procedure that can be used for the search of optimum points on finance applications.
format Online
Article
Text
id pubmed-7512852
institution National Center for Biotechnology Information
language English
publishDate 2018
publisher MDPI
record_format MEDLINE/PubMed
spelling pubmed-75128522020-11-09 Principal Curves for Statistical Divergences and an Application to Finance Rodrigues, Ana Flávia P. Cavalcante, Charles Casimiro Entropy (Basel) Article This paper proposes a method for the beta pricing model under the consideration of non-Gaussian returns by means of a generalization of the mean-variance model and the use of principal curves to define a divergence model for the optimization of the pricing model. We rely on the q-exponential model so consider the properties of the divergences which are used to describe the statistical model and fully characterize the behavior of the assets. We derive the minimum divergence portfolio, which generalizes the Markowitz’s (mean-divergence) approach and relying on the information geometrical aspects of the distributions the Capital Asset Pricing Model (CAPM) is then derived under the geometrical characterization of the distributions which model the data, all by the consideration of principal curves approach. We discuss the possibility of integration of our model into an adaptive procedure that can be used for the search of optimum points on finance applications. MDPI 2018-05-02 /pmc/articles/PMC7512852/ /pubmed/33265423 http://dx.doi.org/10.3390/e20050333 Text en © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Rodrigues, Ana Flávia P.
Cavalcante, Charles Casimiro
Principal Curves for Statistical Divergences and an Application to Finance
title Principal Curves for Statistical Divergences and an Application to Finance
title_full Principal Curves for Statistical Divergences and an Application to Finance
title_fullStr Principal Curves for Statistical Divergences and an Application to Finance
title_full_unstemmed Principal Curves for Statistical Divergences and an Application to Finance
title_short Principal Curves for Statistical Divergences and an Application to Finance
title_sort principal curves for statistical divergences and an application to finance
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512852/
https://www.ncbi.nlm.nih.gov/pubmed/33265423
http://dx.doi.org/10.3390/e20050333
work_keys_str_mv AT rodriguesanaflaviap principalcurvesforstatisticaldivergencesandanapplicationtofinance
AT cavalcantecharlescasimiro principalcurvesforstatisticaldivergencesandanapplicationtofinance