Multivariate skew-normal distributions with applications in insurance. (English) Zbl 1132.91501
Summary: We discuss the skew-normal distribution as an alternative to the classical normal one in the context of both risk measurement and capital allocation. As main risk measure, we consider the tail conditional expectation (TCE). Hence, we investigate an allocation formula based on the TCE, but we also consider S. Wang’s [A set of new methods and tools for enterprise risk capital management and portfolio optimization. Working paper 2002. http://www.casact.com/pubs/forum/02sforum/02sf043.pdf] allocation formula.
MSC:
| 91B30 | Risk theory, insurance (MSC2010) |
| 62E10 | Characterization and structure theory of statistical distributions |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
Software:
snReferences:
| [1] | Arnold, B. C.; Beaver, R. J., Skewed multivariate models related to hidden truncation and/or selective reporting, Sociedad de Estadistica e Investigacion Operativa Test, 11, 1, 7-54 (2002) · Zbl 1033.62013 |
| [2] | Artzner, P.; Delbaen, F.; Eber, J. M.; Heath, D., Coherent measures of risk, Mathematical Finance, 9, 203-228 (1999) · Zbl 0980.91042 |
| [3] | Azzalini, A., A class of distributions which includes the normal ones, Scandinavian Journal of Statistics, 12, 171-178 (1985) · Zbl 0581.62014 |
| [4] | Azzalini, A., The skew-normal distribution and related multivariate families, Scandinavian Journal of Statistics, 32, 159-188 (2005) · Zbl 1091.62046 |
| [5] | Azzalini, A.; Dalla Valle, A., The multivariate skew-normal distribution, Biometrika, 83, 715-726 (1996) · Zbl 0885.62062 |
| [6] | Bellman, R., Introduction to Matrix Analysis (1970), McGraw-Hill: McGraw-Hill New York · Zbl 0216.06101 |
| [7] | Branco, M. D.; Dey, D. K., A general class of multivariate skew-elliptical distributions, Journal of Multivariate Analysis, 79, 99-113 (2001) · Zbl 0992.62047 |
| [8] | Denault, M., 2001. Coherent allocation of risk capital. Working paper. Ecole des H.E.C., Montreal.; Denault, M., 2001. Coherent allocation of risk capital. Working paper. Ecole des H.E.C., Montreal. |
| [9] | Dhaene, J.; Goovaerts, M. J.; Kaas, R., Economic capital allocation derived from risk measures, North American Actuarial Journal, 7, 44-59 (2003) · Zbl 1084.91515 |
| [10] | Landsman, Z.; Valdez, E. A., Tail conditional expectations for elliptical distributions, North American Actuarial Journal, 7, 55-71 (2003) · Zbl 1084.62512 |
| [11] | Landsman, Z.; Valdez, E. A., Tail conditional expectations for exponential dispersion models, ASTIN Bulletin, 35, 189-209 (2005) · Zbl 1099.62122 |
| [12] | Lane, M. N., Pricing risk transfer transactions, ASTIN Bulletin, 30, 2, 259-293 (2000) |
| [13] | Myers, S. C.; Read, J. A., Capital allocation for insurance companies, Journal of Risk and Insurance, 68, 545-580 (2001) |
| [14] | Panjer, H. H., Measurement of risk, solvency requirements and allocation of capital within financial conglomerates, (Proceedings of the 27th International Congress of Actuaries. Proceedings of the 27th International Congress of Actuaries, Cancun (2002)), see also www.stats.uwaterloo.ca/Stats_Dept/IIPR/2001-reports/IIPR-01-15.pdf |
| [15] | Valdez, E. A.; Chernih, A., Wang’s capital allocation formula for elliptically contoured distributions, Insurance: Mathematics and Economics, 33, 517-532 (2003) · Zbl 1103.91375 |
| [16] | Vernic, R., 2004. On the multivariate Skew-Normal distribution and its scale mixtures. Working paper 2/2004 (www.univ-ovidius.ro/math/facultate/preprinturi/CSAM/prepr_csam_02_2004.pdf; Vernic, R., 2004. On the multivariate Skew-Normal distribution and its scale mixtures. Working paper 2/2004 (www.univ-ovidius.ro/math/facultate/preprinturi/CSAM/prepr_csam_02_2004.pdf · Zbl 1108.62052 |
| [17] | Wang, S., 2002. A set of new methods and tools for enterprise risk capital management and portfolio optimization. Working paper. SCOR reinsurance company (www.casact.com/pubs/forum/02sforum/02sf043.pdf; Wang, S., 2002. A set of new methods and tools for enterprise risk capital management and portfolio optimization. Working paper. SCOR reinsurance company (www.casact.com/pubs/forum/02sforum/02sf043.pdf |
| [18] | Yang, H., Esscher transform, Encyclopedia of Actuarial Science (2004), Wiley: Wiley Chichester, pp. 617-621 |
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