Stein's Lemma for elliptical random vectors

Journal of Multivariate Analysis

Volumn 99, Issue 5, 2008, Pages 912-927

  Landsman, Zinoviy ^a   Nešlehová, Johanna ^b  

^a UNIVERSITY OF HAIFA   (Israel)

^b ETH ZURICH   (Switzerland)

Author keywords

Density generator; Elliptical distribution; Generalized hyperbolic distribution; Normal distribution; Normal mixtures; Pearson Type VII distribution; Spherical distribution; Stein's Lemma; Student t distribution

Indexed keywords

EID: 40749116351     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2007.05.006     Document Type: Article

References (18)

1. Bingham N.H., and Kiesel R. Semi-parametric modelling in finance: theoretical foundations. Quant. Finance 2 241-250 (2002)
2. Cambanis S., Huang S., and Simons G. On the theory of elliptically contoured distributions. J. Multivariate Anal. 11 (1981) 368-385
3. Cochrane J.H. Asset Pricing (2001), Princeton University Press, Princeton
4. Embrechts P., Klüppelberg C., and Mikosch T. Modelling Extremal Events for Insurance and Finance (1997), Springer, Berlin
5. Embrechts P., McNeil A.J., and Straumann D. Correlation and dependence in risk management: properties and pitfalls. In: Dempster M.A.H. (Ed). Risk Management: Value at Risk and Beyond (2002), Cambridge University Press, Cambridge 176-223
6. Fang K.-T., Kotz S., and Ng K.-W. Symmetric Multivariate and Related Distributions (1990), Chapman & Hall, New York
7. Fang K.-T., and Zhang Y.-T. Generalized Multivariate Analysis (1990), Springer, Science Press, Berlin, Beijing
8. Froot K.A. Risk management, capital budgeting and capital structure policy for insurers and reinsurers. J. Risk Insurance 74 2 (2007) 273-299
9. M. Hamada, E. Valdez, CAPM and option pricing with elliptical distributions, University of Technology, Sydney, 2004, preprint.
10. Ingersoll J.E. Theory of Financial Decision Making (1987), Rowman & Littlefield, Lanham
11. Kano Y. Consistency property of elliptical probability density functions. J. Multivariate Anal. 51 (1994) 139-147
12. Kelker D. Distribution theory of spherical distributions and a location-scale parameter generalization. Sankhyā A 32 (1970) 419-430
13. Landsman Z. On the generalization of Stein's Lemma for elliptical class of distributions. Statist. Probab. Lett. 76 (2006) 1012-1016
14. Landsman Z., and Valdez E. Tail conditional expectations for elliptical distributions. North Amer. Actuar. J. 7 4 (2003) 55-71
15. McNeil A.J., Frey R., and Embrechts P. Quantitative Risk Management: Concepts, Techniques and Tools (2005), Princeton University Press, Princeton
16. Owen J., and Rabinovitch R. On the class of elliptical distributions and their applications to the theory of portfolio choice. J. Finance 38 3 (1983) 745-752
17. In: Panjer H.H., et al. (Ed). Financial Economics: With Applications to Investments, Insurance and Pensions (1998), The Actuarial Foundation, Schaumburg, IL
18. Stein C.M. Estimation of the mean of a multivariate normal distribution. Ann. Statist. 9 6 (1981) 1135-1151