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The connection between distortion risk measures and ordered weighted averaging operators

  • Jaume Belles-Sampera

    ()

    (Faculty of Economics, University of Barcelona)

  • José M. Merigó

    ()

    (Faculty of Economics, University of Barcelona)

  • Montserrat Guillén

    ()

    (Faculty of Economics, University of Barcelona)

  • Miguel Santolino

    ()

    (Faculty of Economics, University of Barcelona)

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and nite random variables is presented. This connection o ers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed.

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File URL: http://www.ub.edu/irea/working_papers/2012/201201.pdf
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Paper provided by University of Barcelona, Research Institute of Applied Economics in its series IREA Working Papers with number 201201.

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Length: 31 pages
Date of creation: Jan 2012
Date of revision: Jan 2012
Handle: RePEc:ira:wpaper:201201
Contact details of provider: Postal: Tinent Coronel Valenzuela, Num 1-11 08034 Barcelona
Web page: http://www.ub.edu/irea/

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  1. Vicente Royuela & Diona Lambiri & Bianca Biagi, 2006. "Economía Urbana y calidad de vida. Una revisión del estado del conocimiento en España," Working Papers CREAP2006-13, Xarxa de Referència en Economia Aplicada (XREAP), revised Dec 2006.
  2. Kim, Joseph H.T., 2010. "Bias correction for estimated distortion risk measure using the bootstrap," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 198-205, October.
  3. Wang, Shaun & Dhaene, Jan, 1998. "Comonotonicity, correlation order and premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 235-242, July.
  4. Marichal, Jean-Luc, 2004. "Tolerant or intolerant character of interacting criteria in aggregation by the Choquet integral," European Journal of Operational Research, Elsevier, vol. 155(3), pages 771-791, June.
  5. Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2011. "Stochastic comparisons of distorted variability measures," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 11-17, July.
  6. Artís, Manuel & Ramos, Raul & Surinach, Jordi, 2007. "Job Losses, Outsourcing and Relocation: Empirical Evidence Using Microdata," IZA Discussion Papers 2978, Institute for the Study of Labor (IZA).
  7. Juan Carlos Duque & Vicente Royuela & Jordi Suriñach, 2006. "Patrones de publicación internacional (ssci) de los autores afiliados a universidades españolas, en el ámbito económico-empresarial (1994-2004)," IREA Working Papers 200609, University of Barcelona, Research Institute of Applied Economics, revised Dec 2006.
  8. Fabio Manca, 2011. "The "farthest" need the best. Human capital composition and development-specific economic growth," IREA Working Papers 201117, University of Barcelona, Research Institute of Applied Economics, revised Oct 2011.
  9. Kaluszka, Marek & Krzeszowiec, Michał, 2012. "Pricing insurance contracts under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 159-166.
  10. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  11. Wang, Shaun S. & Young, Virginia R. & Panjer, Harry H., 1997. "Axiomatic characterization of insurance prices," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 173-183, November.
  12. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
  13. Jordi Perdiguero, 2011. "Vertical relations and local competition: an empirical approach," IREA Working Papers 201124, University of Barcelona, Research Institute of Applied Economics, revised Dec 2011.
  14. Daniel Albalate & Germa Bel & Xavier Fageda, 2007. "Privatization and regulation of toll motorways in europe," IREA Working Papers 200704, University of Barcelona, Research Institute of Applied Economics, revised Mar 2007.
  15. Juan Carlos Duque & Raúl Ramos & Jordi Suriñach, 2007. "Supervised Regionalization Methods: A Survey," International Regional Science Review, , vol. 30(3), pages 195-220, July.
  16. Vicente Royuela & Manuel Sanchis, 2010. "La reforma de la contratación en el mercado de trabajo: entre la flexibilidad y la seguridad," IREA Working Papers 201006, University of Barcelona, Research Institute of Applied Economics, revised Mar 2010.
  17. Juan Luis Jiménez & Jordi Perdiguero, 2011. "Does Rigidity of Prices Hide Collusion?," IREA Working Papers 201120, University of Barcelona, Research Institute of Applied Economics, revised Oct 2011.
  18. Vicente Royuel & Rosina Moreno & Esther Vaya, 2007. "Is the influence of quality of life on urban growth non-stationary in space? A case study of Barcelona," IREA Working Papers 200703, University of Barcelona, Research Institute of Applied Economics, revised Feb 2007.
  19. Francesca Arnaboldi & Peter Claeys, 2008. "Internet Banking in Europe: a comparative analysis," IREA Working Papers 200811, University of Barcelona, Research Institute of Applied Economics, revised Sep 2008.
  20. Raul Ramos & Jordi Suriñach & Manuel Artís, 2010. "Human capital spillovers, productivity and regional convergence in Spain," Papers in Regional Science, Wiley Blackwell, vol. 89(2), pages 435-447, 06.
  21. Fageda, Xavier & Flores-Fillol, Ricardo, 2012. "Air services on thin routes: Regional versus low-cost airlines," Regional Science and Urban Economics, Elsevier, vol. 42(4), pages 702-714.
  22. Juan Luis Jiménez & Jordi Perdiguero & Ancor Suárez, 2011. "Debating as a classroom tool for adapting learning outcomes to the European higher education area," IREA Working Papers 201109, University of Barcelona, Research Institute of Applied Economics, revised Jun 2011.
  23. António Afonso & Peter Claeys & Ricardo Sousa, 2011. "Fiscal regime shifts in Portugal," Portuguese Economic Journal, Springer, vol. 10(2), pages 83-108, August.
  24. Sandra Nieto & Raul Ramos, 2011. "“¿La sobreeducación de los padres afecta al rendimiento académico de sus hijos?”," IREA Working Papers 201104, University of Barcelona, Research Institute of Applied Economics, revised Apr 2011.
  25. Peter Claeys & Raúl Ramos & Jordi Suriñach, 2007. "Fiscal Sustainability Across Government Tiers," Working Papers XREAP2007-14, Xarxa de Referència en Economia Aplicada (XREAP), revised 2007.
  26. Anwar, Sajid & Zheng, Mingli, 2012. "Competitive insurance market in the presence of ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 79-84.
  27. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2010. "A note on additive risk measures in rank-dependent utility," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 187-189, October.
  28. Manca, Fabio, 2010. "Technology catch-up and the role of institutions," Journal of Macroeconomics, Elsevier, vol. 32(4), pages 1041-1053, December.
  29. Enrique López-Bazo & Burhan Can Karahasan, 2011. "The Spatial Distribution of Human Capital: Can It Really Be Explained by Regional Differences in Market Access?," IREA Working Papers 201102, University of Barcelona, Research Institute of Applied Economics, revised Feb 2011.
  30. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  31. Vicente Royuela & Jordi Lopez-Tamayo & Jordi Suriñach, 2007. "The institutional vs. the academic definition of the quality of work life. What is the focus of the European Commission?," IREA Working Papers 200713, University of Barcelona, Research Institute of Applied Economics, revised Jul 2007.
  32. Daniel Albalate & Germà Bel, 2009. "Factors explaining urban transport systems in large European cities: A cross-sectional approach," IREA Working Papers 200905, University of Barcelona, Research Institute of Applied Economics, revised Apr 2009.
  33. Josep Lluís Carrion-i-Silvestre & Vicente German-Soto, 2008. "Panel Data Stochastic Convergence Analysis of the Mexican Regions," IREA Working Papers 200805, University of Barcelona, Research Institute of Applied Economics, revised Apr 2008.
  34. Marta Gómez-Puig & Simón Sosvilla-Rivero, 2011. "Causality and contagion in peripheral EMU public debt markets: A dynamic approach," Working Papers 11-06, Asociación Española de Economía y Finanzas Internacionales.
  35. Goovaerts, Marc & Linders, Daniël & Van Weert, Koen & Tank, Fatih, 2012. "On the interplay between distortion, mean value and Haezendonck–Goovaerts risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 10-18.
  36. Raul Ramos & Jordi Suriñach & Manuel Artís, 2009. "Regional Economic Growth And Human Capital: The Role Of Overeducation," IREA Working Papers 200904, University of Barcelona, Research Institute of Applied Economics, revised Mar 2009.
  37. Fabio Manca, 2009. "Appropriate IPRs, Human Capital Composition and Economic Growth," IREA Working Papers 200914, University of Barcelona, Research Institute of Applied Economics, revised Jun 2009.
  38. Isabel Cortés-Jiménez & Manuela Pulina & Carme Riera i Prunera & Manuel Artís, 2009. "Tourism and Exports as a means of Growth," IREA Working Papers 200910, University of Barcelona, Research Institute of Applied Economics, revised May 2009.
  39. Sung, K.C.J. & Yam, S.C.P. & Yung, S.P. & Zhou, J.H., 2011. "Behavioral optimal insurance," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 418-428.
  40. Bleichrodt, Han & Eeckhoudt, Louis, 2006. "Survival risks, intertemporal consumption, and insurance: The case of distorted probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 335-346, April.
  41. Montserrat Guillen & Jens Perch Nielsen & Tomas Scheike & Ana Maria Perez-Marin, 2006. "Time-varying effects when analysing customer lifetime duration, application to the insurance market," IREA Working Papers 200604, University of Barcelona, Research Institute of Applied Economics, revised Dec 2006.
  42. Wu, Xianyi & Zhou, Xian, 2006. "A new characterization of distortion premiums via countable additivity for comonotonic risks," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 324-334, April.
  43. Peter Claeys & Fabio Manca, 2011. "A missing spatial link in institutional quality," Applied Economics Letters, Taylor & Francis Journals, vol. 18(3), pages 223-227.
  44. Daniel Albalate & Germà Bel & Joan Calzada, 2010. "Urban transport governance reform in Barcelona," IREA Working Papers 201009, University of Barcelona, Research Institute of Applied Economics, revised Jun 2010.
  45. Denuit Michel & Dhaene Jan & Goovaerts Marc & Kaas Rob & Laeven Roger, 2006. "Risk measurement with equivalent utility principles," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 25, July.
  46. Ramos, Raul & Duque, Juan Carlos & Surinach, Jordi, 2009. "Is the Wage Curve Formal or Informal? Evidence for Colombia," IZA Discussion Papers 4461, Institute for the Study of Labor (IZA).
  47. Shapiro, Arnold F., 2004. "Fuzzy logic in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 399-424, October.
  48. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  49. Hurlimann, Werner, 2006. "A note on generalized distortion risk measures," Finance Research Letters, Elsevier, vol. 3(4), pages 267-272, December.
  50. Daniel Albalate & Germa Bel, 2008. "Motorways, tolls and road safety.Evidence from European Panel Data," IREA Working Papers 200802, University of Barcelona, Research Institute of Applied Economics, revised Feb 2008.
  51. Daniel Albalate & Germà Bel, 2010. "Speed limit laws in America: Economics, politics and geography," IREA Working Papers 201002, University of Barcelona, Research Institute of Applied Economics, revised Jan 2010.
  52. Shapiro, Arnold F., 2009. "Fuzzy random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 307-314, April.
  53. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
  54. Vicente Royuela & Jordi Suriñach, 2009. "Quality in work and aggregate productivity," IREA Working Papers 200901, University of Barcelona, Research Institute of Applied Economics, revised Jan 2009.
  55. De Waegenaere, Anja & Kast, Robert & Lapied, Andre, 2003. "Choquet pricing and equilibrium," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 359-370, July.
  56. Handa, Jagdish, 1977. "Risk, Probabilities, and a New Theory of Cardinal Utility," Journal of Political Economy, University of Chicago Press, vol. 85(1), pages 97-122, February.
  57. Juan Carlos Duque & Raúl Ramos & Vicente Royuela, 2011. "Research networks and scientific production in Economics: The recent Spanish Experience," REVISTA ECOS DE ECONOMÍA, UNIVERSIDAD EAFIT.
  58. Vicente Royuela & Gustavo Adolfo García, 2010. "Economic and social convergence in Colombia," IREA Working Papers 201014, University of Barcelona, Research Institute of Applied Economics, revised Sep 2010.
  59. Shapiro, Arnold F., 2002. "The merging of neural networks, fuzzy logic, and genetic algorithms," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 115-131, August.
  60. Ana María Osorio & Catalina Bolancé & Manuela Alcañiz, 2011. "Measuring early childhood health: a composite index comparing Colombian departments," IREA Working Papers 201122, University of Barcelona, Research Institute of Applied Economics, revised Oct 2011.
  61. Ebru Kerimoglu & Burhan Can Karahasan, 2011. "“Geography of talent and regional differences in Spain”," IREA Working Papers 201107, University of Barcelona, Research Institute of Applied Economics, revised Jun 2011.
  62. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2010. "Decision principles derived from risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 294-302, December.
  63. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2011. "Aggregation functions: Means," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00539028, HAL.
  64. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
  65. Jordi Perdiguero-García, 2010. "“Symmetric or asymmetric gasoline prices? A metaanalysis approach”," IREA Working Papers 201013, University of Barcelona, Research Institute of Applied Economics, revised Nov 2010.
  66. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  67. Carmen Florido & Juan Luis Jiménez & Jordi Perdiguero, 2010. "Cómo (no) adaptar una asignatura al EEES: Lecciones desde la experiencia comparada en España," IREA Working Papers 201008, University of Barcelona, Research Institute of Applied Economics, revised Jun 2010.
  68. Daniel Albalate & Germa Bel, 2008. "Shaping urban traffic patterns through congestion charging: What factors drive success or failure?," IREA Working Papers 200801, University of Barcelona, Research Institute of Applied Economics, revised Jan 2008.
  69. David Castells & Vicente Royuela, 2012. "Agglomeration, Inequality and Economic Growth: Cross-section and panel data analysis," ERSA conference papers ersa12p492, European Regional Science Association.
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