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Principal Curves for Statistical Divergences and an Application to Finance

Department of Teleinformatics Engineering, Federal University of Ceará, Fortaleza-CE 60440-900, Brazil
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Entropy 2018, 20(5), 333; https://doi.org/10.3390/e20050333
Received: 22 February 2018 / Revised: 3 April 2018 / Accepted: 4 April 2018 / Published: 2 May 2018
(This article belongs to the Section Information Theory, Probability and Statistics)
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. View Full-Text
Keywords: principal curves; information geometry; deformed exponential; finance application principal curves; information geometry; deformed exponential; finance application
MDPI and ACS Style

Rodrigues, A.F.P.; Cavalcante, C.C. Principal Curves for Statistical Divergences and an Application to Finance. Entropy 2018, 20, 333.

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