On Partial Stochastic Comparisons Based on Tail Values at Risk
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Título: | On Partial Stochastic Comparisons Based on Tail Values at Risk |
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Autor/es: | Bello, Alfonso J. | Mulero, Julio | Sordo, Miguel A. | Suárez-Llorens, Alfonso |
Grupo/s de investigación o GITE: | Grupo de Estadística Aplicada (GESTA) |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Matemáticas |
Palabras clave: | Value at risk | Tail value at risk | Stochastic orders | Financial risk |
Área/s de conocimiento: | Estadística e Investigación Operativa |
Fecha de publicación: | 18-jul-2020 |
Editor: | MDPI |
Cita bibliográfica: | Bello AJ, Mulero J, Sordo MA, Suárez-Llorens A. On Partial Stochastic Comparisons Based on Tail Values at Risk. Mathematics. 2020; 8(7):1181. doi:10.3390/math8071181 |
Resumen: | The tail value at risk at level p, with p∈(0,1), is a risk measure that captures the tail risk of losses and asset return distributions beyond the p quantile. Given two distributions, it can be used to decide which is riskier. When the tail values at risk of both distributions agree, whenever the probability level p∈(0,1), about which of them is riskier, then the distributions are ordered in terms of the increasing convex order. The price to pay for such a unanimous agreement is that it is possible that two distributions cannot be compared despite our intuition that one is less risky than the other. In this paper, we introduce a family of stochastic orders, indexed by confidence levels p0∈(0,1), that require agreement of tail values at risk only for levels p>p0 . We study its main properties and compare it with other families of stochastic orders that have been proposed in the literature to compare tail risks. We illustrate the results with a real data example. |
Patrocinador/es: | Julio Mulero was supported by the Ministerio de Ciencia e Innovación (Spain), with grant number PID2019-103971GB-I00 (AEI/ FEDER, UE). Alfonso J. Bello, Miguel A. Sordo and Alfonso Suárez-Llorens were partially supported by the Ministerio de Economía y Competitividad (Spain), with grant number MTM2017-89577-P, by the 2014-2020 ERDF Operational Programme, by the Consejería de Economía, Conocimiento, Empresas y Universidad (Junta de Andalucía), with project reference FEDER-UCA18-107519, and by the Universidad de Cádiz through its Programa de Fomento e Impulso de la actividad de Investigación y Transferencia. |
URI: | http://hdl.handle.net/10045/108229 |
ISSN: | 2227-7390 |
DOI: | 10.3390/math8071181 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | © 2020 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/). |
Revisión científica: | si |
Versión del editor: | https://doi.org/10.3390/math8071181 |
Aparece en las colecciones: | INV - GESTA - Artículos de Revistas |
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