The complete mixability and convex minimization problems with monotone marginal densities

Journal of Multivariate Analysis

Volumn 102, Issue 10, 2011, Pages 1344-1360

  Wang, Bin ^a   Wang, Ruodu ^b  

^a PEKING UNIVERSITY   (China)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Complete mixability; Monotone densities; Multivariate dependence; Optimal coupling; Variance minimization

Indexed keywords

EID: 79960044436     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2011.05.002     Document Type: Article

References (22)

1. F. Baiocchi, 1991, Un problema di ottimizzatione nella classe di Fréchet. Unpublished Thesis, Facoltà di Scienze Statistiche, Università La Sapienza, Roma.
2. Bertino S. The minimum of the expected value of the product of three random variables in the Frèchet class. Journal of the Italian Statistical Society 1994, 201-211. 1994-1996.
3. Denneberg D. Non-additive Measure and Integral 1994, Kluwer Academic Publishers, Boston.
4. Embrechts P., Lindskog F., McNeil A. Modelling dependence with copulas and applications to risk management. Handbook of Heavy Tailed Distributions in Finance 2003, 329-384. Elsevier Science BV. S.T. Rachev (Ed.).
5. Embrechts P., McNeil A., Straumann D. Correlation and dependence in risk management: properties and pitfalls. Risk Management: Value at Risk and Beyond 2002, 176-223. Cambridge University Press, Cambridge. M. Dempster (Ed.).
6. Embrechts P., Höing A., Juri A. Using copulae to bound the value-at-risk for functions of dependent risks. Finance and Stoch 2003, 7:145-167.
7. Embrechts P., Puccetti G. Bounds for functions of dependent risks. Finance and Stoch 2006, 10:341-352.
8. Embrechts P., Puccetti G. Risk aggregation. Lecture Notes in Statistics 2010, vol. 198. Springer, Berlin, Heidelberg. P. Jaworski (Ed.).
9. Fishman G.S. Variance reduction in simulation studies. Journal of Statistical Computation and Simulation 1972, 1:173-182.
10. Gaffke N., Rüschendorf L. On a class of extremal problems in statistics. Mathamatische Operationsforschung und Statistik, Series Optimization 1981, 12:123-135.
11. Hammersley I.M., Handscomb D.C. Monte Carlo Methods 1964, Methuen, London.
12. Joe H. Multivariate Models and Dependence Concepts 1997, Chapman & Hall, London.
13. Kaas R., Goovaerts M., Dhaene J., Denuit M. Modern Actuarial Risk Theory 2001, Kluwer Academic Publishers, Boston.
14. M. Knott, C.S. Smith, 1998, On multivariate variance reduction, Unpublished results.
15. Knott M., Smith C.S. Choosing joint distributions so that the variance of the sum is small. Journal of Multivariate Analysis 2006, 97:1757-1765.
16. Nelsen R. An Introduction to Copulas 2006, Springer, New York. second ed.
17. R. Nelsen, M. Ubeda-Flores, 2010, Directional dependence in multivariate distributions, Unpublished results.
18. Rüschendorf L. Inequalities for the expectation of λ-monotone functions. Probability and Related Fields 1980, 54:341-349.
19. Rüschendorf L. Random variables with maximum sums. Advances in Applied Probability 1982, 14:623-632.
20. Rüschendorf L., Uckelmann L. Variance minimization and random variables with constant sum. Distributions with Given Marginals 2002, 211-222. Kluwer. Cuadras (Ed.).
21. Shaked M., Shanthikumar J.G. Stochastic Orders. Springer Series in Statistics 2007.
22. Yang J., Qi Y., Wang R. A class of multivariate copulas with bivariate Fréchet marginal copulas. Insurance: Mathematics and Economics 2009, 45(1):139-147.