Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T22:35:11.849Z Has data issue: false hasContentIssue false
  • English
  • Français

Advances in Complete Mixability

Part of: Mathematical economics Distribution theory - Probability

Published online by Cambridge University Press:  04 February 2016

Giovanni Puccetti ,
Bin Wang  and
Ruodu Wang
Giovanni Puccetti*
Affiliation:
University of Firenze
Bin Wang*
Affiliation:
Peking University
Ruodu Wang*
Affiliation:
Georgia Institute of Technology
*
∗ Postal address: Department of Mathematics for Decision Theory, University of Firenze, via Lombroso 6/17, 50134 Firenze, Italy.
∗∗ Postal address: Department of Mathematics, Peking University, Beijing, 100871, P. R. China.
∗∗∗ Postal address: School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA. Email address: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The concept of complete mixability is relevant to some problems of optimal couplings with important applications in quantitative risk management. In this paper we prove new properties of the set of completely mixable distributions, including a completeness and a decomposition theorem. We also show that distributions with a concave density and radially symmetric distributions are completely mixable.

Keywords

Complete mixabilitymultivariate dependenceconcave densityradially symmetric distributionoptimal coupling

MSC classification

Primary: 60E05: Distributions
Secondary: 91B30: Risk theory, insurance
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 2 , June 2012 , pp. 430 - 440
Copyright
© Applied Probability Trust 

References

Embrechts, P. and Puccetti, G. (2010). Risk aggregation. In Copula Theory and Its Applications (Lecture Notes Statist. 198), eds Bickel, P. et al. Springer, Berlin, pp. 111–126.Google Scholar
Knott, M. and Smith, C. (2006). Choosing Joint distributions so that the variance of the sum is small. J. Multivariate Anal. 97, 1757–1765.Google Scholar
Nelsen, R. B. and Úbeda-Flores, M. (2012). Directional dependence in multivariate distributions. Ann. Inst. Statist. Math. 64, 677–685.CrossRefGoogle Scholar
Rüschendorf, L. and Uckelmann, L. (2002). Variance minimization and random variables with constant sum. In Distributions with Given Marginals and Statistical Modelling, Dordrecht, Kluwer, pp. 211–222.Google Scholar
Wang, B. and Wang, R. (2011). The complete mixability and convex minimization problems with monotone marginal densities. J. Multivariate Anal. 102, 1344–1360.Google Scholar
Wang, R., Peng, L. and Yang, J. (2011). Bounds for the sum of dependent risks and worst Value-at-Risk with monotone marginal densities. Preprint, Georgia Institute of Technology.Google Scholar