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Approximations of Copulas via Transformed Moments

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Abstract

We study the problem of approximating the copula and copula density function from a sequence of transformed moments. In particular, when frequency moments of an underlying bivariate distribution are available, the uniform convergence of the reconstructed copula and the rate of approximation of the copula density function are obtained. Finally, the accuracies of the approximation and estimation are illustrated in a simulation study.

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Acknowledgements

Part of this research has been done while the first author was visiting during his sabbatical leave in October-November, 2017, the Department of Actuarial Science at the University of Lausanne and ISFA at University Lyon 1. He is greatful for the hospitality at both places. The authors are thankful to the anonymous referee for his comments and suggestions which led to a better presentation of the paper.

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Authors and Affiliations

  1. School of Mathematical and Data Sciences, West Virginia University, P.O. Box 6310, Morgantown, WV, 26506, USA

    Robert M. Mnatsakanov

  2. Department of Actuarial Science, Faculty of Business and Economics (HEC), University of Lausanne, Lausanne, Switzerland

    Hansjoerg Albrecher

  3. Swiss Finance Institute, Lausanne, Switzerland

    Hansjoerg Albrecher

  4. Université de Lyon, Université Claude Bernard Lyon 1, Laboratoire de Sciences Actuarielle et Financière, ISFA, 50 Av. Tony Garnier, Lyon, 69007, France

    Stephane Loisel

Authors
  1. Robert M. Mnatsakanov
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  2. Hansjoerg Albrecher
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  3. Stephane Loisel
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Correspondence to Robert M. Mnatsakanov.

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Mnatsakanov, R.M., Albrecher, H. & Loisel, S. Approximations of Copulas via Transformed Moments. Methodol Comput Appl Probab 24, 3175–3193 (2022). https://doi.org/10.1007/s11009-022-09969-8

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  • DOI: https://doi.org/10.1007/s11009-022-09969-8

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