Bernstein Copulas and Composite Bernstein Copulas

  • Jingping Yang
  • Fang WangEmail author
  • Zongkai Xie
Part of the Mathematical Lectures from Peking University book series (MLPKU)


Copula functions have been widely used in econometrics, finance, statistics, and social science for modeling dependence. Reference [42] presented the Bernstein copulas for approximating copula functions. Inspired by the Bernstein copula put forward by [42], reference [48] introduced a new copula function, named as composite Bernstein copula. The composite Bernstein copulas include Bernstein copulas as its special family. Following [48]’s work, [20] discussed the composite Bernstein copula from its generality, its probability structure, and its application in portfolio credit risk. This paper serves as a summary of main results in the above papers.


Bernstein copulas Composite Bernstein copulas 



The authors would like to thank the anonymous reviewer for his constructive comments and suggestions that have led to improvements in the paper. The research work described in the paper was partly supported by the National Natural Science Foundation of China (Grants No.11671021, No.11471222), Capacity Building for Sci-Tech Innovation - Fundamental Scientific Research Funds (No. 025185305000/204) and Youth Innovative Research Team of Capital Normal University.


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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.LMEQF, Department of Financial MathematicsPeking UniversityBeijingChina
  2. 2.School of Mathematical SciencesCapital Normal UniversityBeijingChina
  3. 3.Department of Financial MathematicsPeking UniversityBeijingChina

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