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Open AccessArticle

Tsallis Entropy for Cross-Shareholding Network Configurations

1
Department of Social and Economic Sciences, Sapienza University of Rome, p.le A. Moro 5, 00185 Roma, Italy
2
School of Business, London South Bank University, London SE1 0AA, UK
3
Department of Statistical Sciences, Sapienza University of Rome, p.le A. Moro 5, 00185 Roma, Italy
4
School of Business, College of Social Sciences, Arts, and Humanities, Brookfield, University of Leicester, Leicester LE2 1RQ, UK
5
Group of Researchers for Applications of Physics in Economy and Sociology (GRAPES), Rue de la belle jardinière, 483, Sart Tilman, B-4031 Angleur, Liege, Belgium
6
Department of Statistics and Econometrics, Bucharest University of Economic Studies, Calea Dorobantilor 15-17, 010552 Sector 1 Bucharest, Romania
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(6), 676; https://doi.org/10.3390/e22060676
Received: 27 May 2020 / Revised: 13 June 2020 / Accepted: 13 June 2020 / Published: 17 June 2020
(This article belongs to the Special Issue Complexity in Economic and Social Systems)
In this work, we develop the Tsallis entropy approach for examining the cross-shareholding network of companies traded on the Italian stock market. In such a network, the nodes represent the companies, and the links represent the ownership. Within this context, we introduce the out-degree of the nodes—which represents the diversification—and the in-degree of them—capturing the integration. Diversification and integration allow a clear description of the industrial structure that were formed by the considered companies. The stochastic dependence of diversification and integration is modeled through copulas. We argue that copulas are well suited for modelling the joint distribution. The analysis of the stochastic dependence between integration and diversification by means of the Tsallis entropy gives a crucial information on the reaction of the market structure to the external shocks—on the basis of some relevant cases of dependence between the considered variables. In this respect, the considered entropy framework provides insights on the relationship between in-degree and out-degree dependence structure and market polarisation or fairness. Moreover, the interpretation of the results in the light of the Tsallis entropy parameter gives relevant suggestions for policymakers who aim at shaping the industrial context for having high polarisation or fair joint distribution of diversification and integration. Furthermore, a discussion of possible parametrisations of the in-degree and out-degree marginal distribution—by means of power laws or exponential functions— is also carried out. An empirical experiment on a large dataset of Italian companies validates the theoretical framework. View Full-Text
Keywords: Tsallis entropy; copula functions; cross-shareholding network; finance Tsallis entropy; copula functions; cross-shareholding network; finance
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Cerqueti, R.; Rotundo, G.; Ausloos, M. Tsallis Entropy for Cross-Shareholding Network Configurations. Entropy 2020, 22, 676.

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