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Publisher: Springer

Issued date: 2009-09

Citation: Methodology and Computing in Applied Probability, sept. 2009, v. 11, nº 3, pp: 385-399.

ISSN: 1387-5841

DOI: 10.1007-s11009-008-9089-z

Sponsor: This research was partially funded by Welzia Management, SGIIC SA,RD Sistemas SA, Comunidad Autónoma de Madrid Grant s-0505-tic-000230,and MEyC Grant BEC2000-1388-C04-03 and by the Natural Sciences and EngineeringResearch Council of Canada NSERC Grant 36860-06.

Publisher version: http:-dx.doi.org-10.1007-s11009-008-9089-z

Keywords: Risk measures , Distortion functions , Coherent measures , Complete measures , Adapted measures

Abstract:The current literature does not reach a consensus on which risk measures should be used in practice. Our objective is to give at least a partial solution to this problem. We study properties that a risk measure must satisfy to avoid inadequate portfolio selectThe current literature does not reach a consensus on which risk measures should be used in practice. Our objective is to give at least a partial solution to this problem. We study properties that a risk measure must satisfy to avoid inadequate portfolio selections. The properties that we propose for risk measures can help avoid the problems observed with popular measures, like Value at Risk VaRα or ConditionalVaRα CVaRα. This leads to the definition of two new families: complete and adapted risk measures. Our focus is on risk measures generated by distortion functions. Two new properties are put forward for these: completeness, ensuring that the distortion risk measure uses all the information of the loss distribution, and adaptability, forcing the measure to use this information adequately.+-





Author: Balbás, Alejandro; Garrido, José; Mayoral, Silvia

Source: http://e-archivo.uc3m.es


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Universidad Carlos III de Madrid Repositorio institucional e-Archivo http:--e-archivo.uc3m.es Departamento de Economía de la Empresa DEE - Artículos de Revistas 2009-09 Properties of Distortion Risk Measures Balbás, Alejandro Springer Methodology and Computing in Applied Probability, sept.
2009, v.
11, nº 3, pp: 385-399. http:--hdl.handle.net-10016-14071 Descargado de e-Archivo, repositorio institucional de la Universidad Carlos III de Madrid Properties of Distortion Risk Measures Alejandro Balbás · José Garrido · Silvia Mayoral Abstract The current literature does not reach a consensus on which risk measures should be used in practice.
Our objective is to give at least a partial solution to this problem.
We study properties that a risk measure must satisfy to avoid inadequate portfolio selections.
The properties that we propose for risk measures can help avoid the problems observed with popular measures, like Value at Risk (VaRα ) or Conditional VaRα (CVaRα ).
This leads to the definition of two new families: complete and adapted risk measures.
Our focus is on risk measures generated by distortion functions.
Two new properties are put forward for these: completeness, ensuring that the distortion risk measure uses all the information of the loss distribution, and adaptability, forcing the measure to use this information adequately. Keywords Risk measures · Distortion functions · VaRα · CVaRα · Coherent measures · Complete measures · Adapted measures AMS 2000 Subject Classification 62P05 · 91B28 This research was partially funded by1,3 Welzia Management, SGIIC SA, RD Sistemas SA, Comunidad Autónoma de Madrid Grant s-0505-tic-000230, and MEyC Grant BEC2000-1388-C04-03 and by2 the Natural Sciences and Engineering Research Council of Canada (NSERC) Grant 36860-06. A.
Balbás Universidad Carlos III de Madrid, Madrid, Spain e-mail: balbas@emp.uc3m.es J.
Garrido (B) Concordia University, Montreal, Canada e-mail: garrido@mathstat.concordia.ca S...





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