Skewed bivariate models and nonparametric estimation for the CTE risk measure

Insurance: Mathematics and Economics

Volumn 43, Issue 3, 2008, Pages 386-393

  Bolance, Catalina ^a   Guillen, Montserrat ^a   Pelican, Elena ^b   Vernic, Raluca ^b  

^a UNIVERSITY OF BARCELONA   (Spain)

^b OVIDIUS UNIVERSITY   (Romania)

Author keywords

Bivariate distributions; Conditional tail expectation; Kernel estimation

Indexed keywords

EID: 56749154445     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.insmatheco.2008.07.005     Document Type: Article

References (34)

1. Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control 19 (1974) 716-723
2. Arnold B.C., and Beaver R.J. Skewed multivariate models related to hidden truncation and/or selective reporting. Sociedad de Estadistica e Investigacion Operativa Test 11 (2002) 7-54
3. Artzner P., Delbaen F., Eber J.M., and Heath D. Coherent measures of risk. Mathematical Finance 9 (1999) 203-228
4. Azzalini A. A note on the estimation of a distribution function and quantiles by kernel method. Biometrika 68 (1981) 226-228
5. Azzalini A. A class of distributions which includes the normal ones. Scandinavian Journal of Statistics 12 (1985) 171-178
6. Azzalini A. The skew-normal distribution and related multivariate families. Scandinavian Journal of Statistics 32 (2005) 159-188
7. Azzalini A., and Capitanio A. Statistical applications of the multivariate skew-normal distribution. Journal of the Royal Statistical Society, Series B 61 (1999) 579-602
8. Azzalini A., Dal Cappello T., and Kotz S. Log-skew-normal and log-skew-t distributions as models for family income data. Journal of Income Distribution 11 (2003) 12-20
9. Azzalini A., and Dalla Valle A. The multivariate skew-normal distribution. Biometrika 83 (1996) 715-726
10. Bolancé C., Guillén M., and Nielsen J.P. Kernel density estimation of actuarial loss functions. Insurance: Mathematics and Economics 32 (2003) 19-36
11. Bolancé C., Guillén M., and Nielsen J.P. Inverse Beta transformation in kernel density estimation. Statistics & Probability Letters 78 (2008) 1757-1764
12. Bourden R.L., and Faires J.D. Numerical Analysis. 7th edition (2001), Brooks/Cole, Pacific Grove
13. Buch A., and Dorfleitner G. Coherent risk measures, coherent capital allocations and the gradient allocation principle. Insurance: Mathematics and Economics 42 (2008) 235-242
14. Buch-Larsen T., Guillen M., Nielsen J.P., and Bolancé C. Kernel density estimation for heavy-tailed distributions using the Champernowne transformation. Statistics 39 (2005) 503-518
15. Clements A.E., Hurn A.S., and Lindsay K.A. Möbius-like mappings and their use in kernel density estimation. Journal of the American Statistical Association 98 (2003) 993-1000
16. Chen S.X. Probability density function estimation using Gamma kernels. Annals of the Institute of Statistical Mathematics 52 (2000) 471-480
17. Chiragiev A., and Landsman Z. Multivariate Pareto portfolios: TCE-based capital allocation and divided differences. Scandinavian Actuarial Journal 4 (2007) 261-280
18. Denault, M., 2001. Coherent allocation of risk capital. Working Paper. Ecole des H.E.C., Montreal
19. Dhaene J., Goovaerts M.J., and Kaas R. Economic capital allocation derived from risk measures. North American Actuarial Journal 7 (2003) 44-59
20. Dhaene J., Henrard L., Landsman Z., Vandendorpe A., and Vanduffel S. Some results on the CTE-based capital allocation rule. Insurance: Mathematics and Economics 42 (2008) 855-863
21. Dhaene J., Laeven R.J.A., Vanduffel S., Darkiewicz G., and Goovaerts M.J. Can a coherent risk measure be too subadditive?. Journal of Risk & Insurance 75 (2008) 365-386
22. Furman E., and Landsman Z. Risk capital decomposition for a multivariate dependent gamma portfolio. Insurance: Mathematics and Economics 37 (2005) 635-649
23. Furman E., and Zitikis R. Weighted premium calculation principles. Insurance: Mathematics and Economics 42 (2008) 459-465
24. Gupta A.K., Gonzalez-Farias G., and Dominguez-Molina J.A. A multivariate skew normal distribution. Journal of Multivariate Analysis 89 (2004) 181-190
25. Landsman Z., and Valdez E.A. Tail conditional expectation for exponential dispersion models. Astin Bulletin 35 (2005) 189-209
26. Mladenovic N., and Hansen P. Variable neighborhood search. Computers and Operations Research 24 (1997) 1097-1100
27. Panjer, H.H., 2002. Measurement of risk, solvency requirements and allocation of capital within financial conglomerates. In: 27th International Congress of Actuaries. Cancun
28. Reiss R.D. Nonparametric estimation of smooth distribution functions. Scandinavian Journal of Statistics 8 (1981) 116-119
29. Scott D.W. Multivaraite Density Estimation. Theory, Practice and Visualization (1992), John Wiley & Sons, Inc
30. Valdez E.A., and Chernih A. Wang's capital allocation formula for elliptically contoured distributions. Insurance: Mathematics and Economics 33 (2003) 517-532
31. Vernic R. Multivariate skew-normal distributions with applications in insurance. Insurance: Mathematics and Economics 38 (2006) 413-426
32. Wand P., and Jones M.C. Kernel Smoothing (1995), Chapman & Hall
33. Wand P., Marron J.S., and Ruppert D. Transformations in density estimation. Journal of the American Statistical Association 86 (1991) 343-361
34. Wang, S., 2002. A set of new methods and tools for enterprise risk capital management and portfolio optimization. Working Paper. SCOR reinsurance company. http://www.casact.com/pubs/forum/02sforum/02sf043.pdf