Modelling losses and locating the tail with the Pareto Positive Stable distribution

Insurance: Mathematics and Economics

Volumn 49, Issue 3, 2011, Pages 454-461

  Guillen, Montserrat ^a   Prieto, Faustino ^b   Sarabia, José María ^b  

^a UNIVERSITY OF BARCELONA   (Spain)

^b UNIVERSITY OF CANTABRIA   (Spain)

Author keywords

Loss model; Pareto distribution; Positive stable law; Severity distribution

Indexed keywords

EID: 80051578463     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.insmatheco.2011.07.004     Document Type: Article

References (32)

1. Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control 1974, 19:716-723.
2. Azzalini A. The skew-normal distribution and related multivariate families (with discussion). Scandinavian Journal of Statistics 2005, 32(2):159-188.
3. Balakrishnan P.V.S., Miller J.M., Shankar S.G. Power laws and evolutionary trends in stock markets. Economics Letters 2008, 98(2):194-200.
4. Balakrishnan N., Nevzorov V.B. A Primer on Statistical Distributions 2003, John Wiley, New York.
5. Bauke H. Parameter estimation for power-law distributions by maximum likelihood methods. The European Physical Journal B 2007, 58(2):167-173.
6. Bolancé C., Guillen M., Nielsen J.P. Kernel density estimation of actuarial loss functions. Insurance: Mathematics and Economics 2003, 32(1):19-36.
7. Bolancé C., Guillen M., Pelican E., Vernic R. Skewed bivariate models and nonparametric estimation for the CTE risk measure. Insurance: Mathematics and Economics 2008, 43(3):386-393.
8. Buch-Larsen T., Guillen M., Nielsen J.P., Bolancé C. Kernel density estimation for heavy-tailed distributions using the Champernowne transformation. Statistics 2005, 39(6):503-518.
9. Castillo E., Hadi A.S., Balakrishnan N., Sarabia J.M. Extreme Value and Related Models with Applications in Engineering and Science 2005, John Wiley, New York.
10. Cherubini U., Mulinacci S., Romagnoli S. On the distribution of (un)bounded sum of random variables. Insurance: Mathematics and Economics 2011, 48(1):56-63.
11. Clauset A., Rohilla C., Newman M.E.J. Power-law distributions in empirical data. SIAM Review 2009, 51(4):661-703.
12. Cummins J.D., Dionne G., McDonald J.B., Pritchett B.M. Applications of the GB2 family of distributions in modeling insurance loss processes. Insurance: Mathematics and Economics 1990, 9(4):257-272.
13. Drees H., de Haan L., Resnick S. How to make a Hill plot. Annals of Statistics 2000, 28(1):254-274.
14. Embrechts P., Klüppelberg K., Mikosh T. Modelling Extremal Events for Insurance and Finance 1997, Springer.
15. Feller W. An Introduction to Probability Theory and its Applications 2 1971, John Wiley, New York. 2nd ed.
16. Frangos N., Karlis D. Modelling losses using an exponential-inverse Gaussian distribution. Insurance: Mathematics and Economics 2004, 35(1):53-67.
17. Furman E., Landsman Z. Multivariate Tweedie distributions and some related capital-at-risk analyses. Insurance: Mathematics and Economics 2010, 46(2):351-361.
18. Gabaix X. Zipf's law and the growth of cities. The American Economic Review 1999, 89:129-132.
19. Gabaix X. Zipf's law for cities: An explanation. The Quarterly Journal of Economics 1999, 114:739-767.
20. Gabaix X., Ioannides Y.M. The Evolution of City Size Distributions. Handbook of Regional and Urban Economics 2004, vol. 4:2341-2378. Elsevier, Amsterdam. J.V. Henderson, Y. Thisse (Eds.).
21. Han Z., Gaua W. Estimation of loss reserves with lognormal development factors. Insurance: Mathematics and Economics 2008, 42(1):389-395.
22. Hill B.M. A simple general approach to inference about the tail of a distribution. Annals of Statistics 1975, 3:1163-1174.
23. Johnson N.S., Kotz S., Balakrishnan N. Continuous Univariate Distributions, Vol. I 1994, John Wiley.
24. Johnson N.S., Kotz S., Balakrishnan N. Continuous Univariate Distributions, Vol. II 1995, John Wiley.
25. Klugman S.A., Panjer H.H., Wilmot G.E. Loss Models: From Data to Decisions 2008, John Wiley.
26. Matthys G., Beirlant J. Adaptative Threshold Methods in Tail Index Estimation 2002, 37-49. Risk Books, London. P. Embrechts (Ed.).
27. Melo L.F., Becerra O.R. Medidas de Riesgo, Características y técnicas de medición. Una aplicación del VaR y el ES a la tasa interbancaria de Colombia 2006, Centro Editorial Universidad del Rosario, Bogota, DC, Colombia.
28. Panjer H.H. Operational Risk Modelling Analytics 2006, John Wiley and Son.
29. Reiss R.D., Thomas M. Statistical Analysis of Extreme Values 1997, Birkäuser.
30. Sarabia, J.M., Gómez-Déniz, E., Vázquez, F.J., 2006. Estadística Actuarial. Teoría y Aplicaciones, Pearson Educación.
31. Sarabia J.M., Prieto F. The Pareto-positive stable distribution: a new descriptive method for city size data. Physica A: Statistical Mechanics and its Applications 2009, 388(19):4179-4191.
32. Valdez E.A., Dhaene J., Maj M., Vanduffel S. Bounds and approximations for sums of dependent log-elliptical random variables. Insurance: Mathematics and Economics 2009, 44(3):385-397.