Medidas de riesgo para riesgo operacional con un modelo de perdida agregada de Poisson-Lindley

Agustín Hernández Bastida, Pilar Fernández Sánchez

Resumen


En este trabajo se considera la determinación de medidas de riesgo en riesgo operacional, es decir, la determinación de cuantiles de alto orden. Se considera la aproximación basada en la distribución de la pérdida dentro de la aproximación avanzada. Se calculan, y se comparan entre si, las medidas de riesgo a partir de la distribución de la pérdida agregada y a partir de la distribución predictiva considerando como funciones estructura para los perfiles de riesgo las distribuciones Triangular y Gamma.

This paper considers the determination of the risk measures in Operational Risk, i.e. the determination of a high level quantile. The Loss Distribution Approach in the Advanced Measurement Approach is adopted. The risk measures, obtained from the aggregate loss distribution and from the predictive distribution are determined and compared, using the Triangular and Gamma distributions as structure functions of the risk profiles.

Palabras clave


Modelo de pérdida agregada; Distribución de Poisson-Lindley; Distribución triangular; Distribución gamma; Aggregate Loss Model; Poisson-Lindley distribution; Triangular distribution; Gamma distribution

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Referencias


BIS (2005). Basel II: International convergence of capital measurement and capital standard: A revised framework. Bank for International Settlements (BIS), http://www.bis.org/index.htm

Carrillo-Menéndez, S. y Suarez, A. (2006). “Effective measurement of the operational risk”, Estabilidad financier, Banco de España, 11, pp. 61-90.

Chavez-Demoulin, V.; Embrechts, P. y Neslehová, J. (2006). “Quantitative models for operational risk: Extremes, dependence and aggregation”, Journal of Banking and Finance, 30 (10), pp. 2635-2658.

Cruz, M.G. (2002). Modelling, measuring and hedging operational risk. UK: John Wiley and Sons.

Ghitany, M.E. y Al-Mutairi, D.K. (2008). “Estimation methods for the discrete Poisson-Lindley distribution”, Journal of Statistical Computation and Simulation, 79 (3), pp. 279-287.

Ghitany, M.E.; Al-Mutairi, D.K. y Nadarajah, S. (2009). “Zero-truncated Poisson-Lindley distribution and its application”, Mathematics and Computers in Simulation, 79 (1), pp.1-9.

Grandell, J. (1997). Mixed poisson processes. New York: Chapman and Hall.

Hernández-Bastida, A.; Fernández-Sánchez, M.P y Gómez-Déniz, E (2009). “The net bayes premium with dependence between the risk profiles”, Insurance:Mathematics and Economics, 45, pp. 247-254.

Hernández-Bastida, A.; Fernández-Sánchez, M.P. y Gómez-Déniz, E. (2010). “Collective risk model: Poisson-Lindley and exponential distributions for bayes premium and operational risk”, Journal of Statistical Computation and Simulation, to appear.

Johnson, D. (1997). “The triangular distribution as a proxy for the beta distribution in risk analysis”, Journal of the Royal Stat. Society, Series D (The Statistician), 46 (3), pp. 388-398.

Karlis, D. y Xekalaki, E. (2005). “Mixed poisson distributions”, International Statistical Review, 73, pp. 35-58.

Klugman, S.A.; Panjer, H.H. and Willmot, G.E. (2004). Loss models: From data to decision. New York: Willey and Sons.

Kozubowski, T.J. and Panoska, A.K. (2005). “A mixed bivariate distribution with exponential and geometric marginals”, Journal of Statistical Planning and Inference, 234, pp. 501-520.

Lambrigger, D.D.; Shevchenko, P.V. and Wüthrich, M.V. (2007). “The quantification of operational risk using internal data, relevant external data and expert opinions”, The Journal of Operational Risk, 2-3, pp. 3-27.

Lindley, D.V. (1958). “Fiducial distributions and Bayes’s theorem”, Journal of the Royal Stat. Soc. Series B, 1; pp. 102-107.

McNeil, A.; Frey, R. y Embrechts, P. (2005). Quantitative risk management: Concepts, techniques and tools. New Jersey (USA): Princeton University Press.

Nadarajah, S. y Kotz, S. (2006a). “Compound mixed Poisson distributions I”, Scandinavian Actuarial Journal, 3, pp. 141-162.

Nadarajah, S. y Kotz, S. (2006b). “Compound mixed Poisson distributions II”, Scandinavian Actuarial Journal, 3, pp. 163-181.

Nikoloulopoulos, A.K. y Karlis, D. (2008). “On modelling count data: a comparison of some well-known discrete distributions”, Journal of Statistical Computation and Simulation, 78 (3), pp. 437-457.

Sandström, A. (2006). Solvency: Models, assessment and regulation. Boca Raton (FL): Chapman & Hall/CRC.

Sankaran, M. (1971). “The discrete Poisson-Lindley distribution”, Biometrics, 26 (1), pp. 145-149.

Shevchenko, P.V. (2008). “Estimation of operational risk capital charge under parameter uncertainty”, The Journal of Operational Risk, 1 (3), pp. 51-63.

Shevchenko, P.V. y Wüthrich, M.V. (2006). “The structural modelling of operational risk via bayesian inference: Combining loss data with expert opinions”, The Journal of Operational Risk, 1 (3), pp. 3-26.

Wüthrich, M.V. (2006). “Premium liability risks: Modelling small claims”, Bulletin of the Swiss Association of Actuaries, 1, pp. 27-38.




DOI: http://dx.doi.org/10.18002/pec.v0i11.627

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