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COMPOSITE BERNSTEIN COPULAS

Published online by Cambridge University Press:  11 March 2015

Jingping Yang ,
Zhijin Chen ,
Fang Wang  and
Ruodu Wang
Jingping Yang
Affiliation:
LMEQF, Department of Financial Mathematics, Peking University, Beijing, 100871, China E-Mail: yangjp@math.pku.edu.cn
Zhijin Chen
Affiliation:
Department of Financial Mathematics, School of Mathematical Sciences and Center for Statistical Sciences, Peking University, Beijing, 100871, China E-Mail: bjzhijin@126.com
Fang Wang*
Affiliation:
School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China
Ruodu Wang
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo N2L 3G1, Canada E-Mail: wang@uwaterloo.ca
*
E-Mail: fang72_wang@cnu.edu.cn
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Abstract

Copula function has been widely used in insurance and finance for modeling inter-dependency between risks. Inspired by the Bernstein copula put forward by Sancetta and Satchell (2004, Econometric Theory, 20, 535–562), we introduce a new class of multivariate copulas, the composite Bernstein copula, generated from a composition of two copulas. This new class of copula functions is able to capture tail dependence, and it has a reproduction property for the three important dependency structures: comonotonicity, countermonotonicity and independence. We introduce an estimation procedure based on the empirical composite Bernstein copula which incorporates both prior information and data into the estimation. Simulation studies and an empirical study on financial data illustrate the advantages of the empirical composite Bernstein copula estimation method, especially in capturing tail dependence.

Keywords

Composite Bernstein copulacopula constructiontail dependencenon-parametric estimation
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 45 , Issue 2 , May 2015 , pp. 445 - 475
Copyright
Copyright © ASTIN Bulletin 2015 

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