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Fundamentals of Risk Measurement and Aggregation for Insurance Applications

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Modeling Decisions for Artificial Intelligence (MDAI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9880))

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Abstract

The fundamentals of insurance are introduced and alternatives to risk measurement are presented, illustrating how the size and likelihood of future losses may be quantified. Real data indicate that insurance companies handle many small losses, while large or extreme claims occur only very rarely. The skewness of the profit and loss probability distribution function is especially troublesome for risk quantification, but its strong asymmetry is successfully addressed with generalizations of kernel estimation. Closely connected to this approach, distortion risk measures study the expected losses of a transformation of the original data. GlueVaR risk measures are presented. The notions of subadditivity and tail-subadditivity are discussed and an overview of risk aggregation is given with some additional applications to insurance.

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References

  1. Acerbi, C., Tasche, D.: On the coherence of expected shortfall. J. Bank. Financ. 26(7), 1487–1503 (2002)

    Article  Google Scholar 

  2. Alemany, R., Bolancé, C., Guillen, M.: A nonparametric approach to calculating value-at-risk. Insur. Math. Econ. 52(2), 255–262 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Artzner, P., Delbaen, F., Eber, J.M., Heath, D.: Coherent measures of risk. Math. Financ. 9(3), 203–228 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  4. Balbás, A., Garrido, J., Mayoral, S.: Properties of distortion risk measures. Methodol. Comput. Appl. Probab. 11(3), 385–399 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Belles-Sampera, J., Guillen, M., Santolino, M.: Beyond value-at-risk: GlueVaR distortion risk measures. Risk Anal. 34(1), 121–134 (2014)

    Article  MATH  Google Scholar 

  6. Belles-Sampera, J., Guillen, M., Santolino, M.: GlueVaR risk measures in capital allocation applications. Insur. Math. Econ. 58, 132–137 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  7. Belles-Sampera, J., Guillen, M., Santolino, M.: The use of flexible quantile-based measures in risk assessment. Commun. Stat. Theory Methods 45(6), 1670–1681 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  8. Belles-Sampera, J., Guillen, M., Santolino, M.: What attitudes to risk underlie distortion risk measure choices? Insur. Math. Econ. 68, 101–109 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  9. Belles-Sampera, J., Merigo, J.M., Guillen, M., Santolino, M.: The connection between distortion risk measures and ordered weighted averaging operators. Insur. Math. Econ. 52(2), 411–420 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Bolancé, C., Guillen, M., Nielsen, J.P.: Kernel density estimation of actuarial loss functions. Insur. Math. Econ. 32(1), 19–36 (2003)

    Article  MATH  Google Scholar 

  11. Bolancé, C., Guillen, M., Nielsen, J.P.: Inverse Beta transformation in kernel density estimation. Stat. Probab. Lett. 78(13), 1757–1764 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Bolancé, C., Guillén, M., Nielsen, J.P.: Transformation kernel estimation of insurance claim cost distributions. In: Corazza, M., Pizzi, C. (eds.) Mathematical and Statistical Methods for Actuarial Sciences and Finance, pp. 43–51. Springer, Milan (2010)

    Chapter  Google Scholar 

  13. Bolancé, C., Guillen, M., Pelican, E., Vernic, R.: Skewed bivariate models and nonparametric estimation for the CTE risk measure. Insur. Math. Econ. 43(3), 386–393 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Buch-Larsen, T., Nielsen, J.P., Guillen, M., Bolance, C.: Kernel density estimation for heavy-tailed distributions using the Champernowne transformation. Statistics 39(6), 503–516 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. Choquet, G.: Theory of capacities. Ann. de l’Inst. Fourier 5, 131–295 (1954). Institut Fourier

    Article  MathSciNet  MATH  Google Scholar 

  16. Denneberg, D.: Non-additive Measure and Integral, vol. 27. Springer Science and Business Media, Netherlands (1994)

    Book  MATH  Google Scholar 

  17. Denuit, M., Dhaene, J., Goovaerts, M., Kaas, R.: Actuarial Theory for Dependent Risks: Measures, Orders and Models. Wiley, Hoboken (2006)

    Google Scholar 

  18. Dhaene, J., Laeven, R.J., Vanduffel, S., Darkiewicz, G., Goovaerts, M.J.: Can a coherent risk measure be too subadditive? J. Risk Insur. 75(2), 365–386 (2008)

    Article  Google Scholar 

  19. Guelman, L., Guillen, M., Pérez-Marín, A.M.: A decision support framework to implement optimal personalized marketing interventions. Decis. Support Syst. 72, 24–32 (2015)

    Article  Google Scholar 

  20. Guillen, M.: Riesgo y seguro en economia. Discurso de ingreso en la Real Academia de Ciencias Economicas y Financieras. Barcelona (2015)

    Google Scholar 

  21. Guillen, M., Prieto, F., Sarabia, J.M.: Modelling losses and locating the tail with the Pareto Positive Stable distribution. Insur. Math. Econ. 49(3), 454–461 (2011)

    Article  MathSciNet  Google Scholar 

  22. Guillen, M., Sarabia, J.M., Prieto, F.: Simple risk measure calculations for sums of positive random variables. Insur. Math. Econ. 53(1), 273–280 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  23. Jorion, P.: Value at Risk: The New Benchmark for Managing Financial Risk, vol. 3. McGraw-Hill, New York (2007)

    Google Scholar 

  24. MacKenzie, C.A.: Summarizing risk using risk measures and risk indices. Risk Anal. 34(12), 2143–2162 (2014)

    Article  Google Scholar 

  25. McNeil, A.J., Frey, R., Embrechts, P.: Quantitative Risk Management: Concepts, Techniques and Tools. Princeton University Press, Princeton (2015)

    MATH  Google Scholar 

  26. Szeg, G.: Measures of risk. J. Bank. Financ. 26(7), 1253–1272 (2002)

    Article  Google Scholar 

  27. Tsanakas, A., Desli, E.: Measurement and pricing of risk in insurance markets. Risk Anal. 25(6), 1653–1668 (2005)

    Article  Google Scholar 

  28. Wand, M.P., Marron, J.S., Ruppert, D.: Transformations in density estimation. J. Am. Stat. Assoc. 86(414), 343–353 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  29. Wang, S.: Insurance pricing and increased limits ratemaking by proportional hazards transforms. Insur. Math. Econ. 17(1), 43–54 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  30. Wang, S.: Premium calculation by transforming the layer premium density. Astin Bull. 26(01), 71–92 (1996)

    Article  Google Scholar 

  31. Yaari, M.E.: The dual theory of choice under risk. Econom. J. Econom. Soc. 55, 95–115 (1987)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Econometrics, Riskcenter-IREA, Universitat de Barcelona, Av. Diagonal, 690, 08034, Barcelona, Spain

    Montserrat Guillen, Catalina Bolancé & Miguel Santolino

Authors
  1. Montserrat Guillen
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  2. Catalina Bolancé
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  3. Miguel Santolino
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Corresponding author

Correspondence to Montserrat Guillen .

Editor information

Editors and Affiliations

  1. University of Kövde , Skövde, Sweden

    Vicenç Torra

  2. Toho Gakuen , Kunitachi, Tokyo, Japan

    Yasuo Narukawa

  3. Enginyeria de la Informacio I de les Com, Univ Autonoma de Barcelona, Bellaterra, Spain

    Guillermo Navarro-Arribas

  4. Universitat d'Andorra , Sant Julià de Lòria, Andorra

    Cristina Yañez

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© 2016 Springer International Publishing Switzerland

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Guillen, M., Bolancé, C., Santolino, M. (2016). Fundamentals of Risk Measurement and Aggregation for Insurance Applications. In: Torra, V., Narukawa, Y., Navarro-Arribas, G., Yañez, C. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2016. Lecture Notes in Computer Science(), vol 9880. Springer, Cham. https://doi.org/10.1007/978-3-319-45656-0_2

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  • DOI: https://doi.org/10.1007/978-3-319-45656-0_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45655-3

  • Online ISBN: 978-3-319-45656-0

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