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Correction published on 13 July 2021, see Mathematics 2021, 9(14), 1646.
Article

Adaptive Bernstein Copulas and Risk Management

1
Institute of Mathematics, Carl von Ossietzky Universität Oldenburg, D-26111 Oldenburg, Germany
2
Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska Str. 64, 01601 Kyiv, Ukraine
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(12), 2221; https://doi.org/10.3390/math8122221
Received: 29 October 2020 / Revised: 8 December 2020 / Accepted: 11 December 2020 / Published: 14 December 2020
We present a constructive approach to Bernstein copulas with an admissible discrete skeleton in arbitrary dimensions when the underlying marginal grid sizes are smaller than the number of observations. This prevents an overfitting of the estimated dependence model and reduces the simulation effort for Bernstein copulas a lot. In a case study, we compare different approaches of Bernstein and Gaussian copulas regarding the estimation of risk measures in risk management. View Full-Text
Keywords: copulas; partition-of-unity copulas; Monte Carlo methods copulas; partition-of-unity copulas; Monte Carlo methods
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MDPI and ACS Style

Pfeifer, D.; Ragulina, O. Adaptive Bernstein Copulas and Risk Management. Mathematics 2020, 8, 2221. https://doi.org/10.3390/math8122221

AMA Style

Pfeifer D, Ragulina O. Adaptive Bernstein Copulas and Risk Management. Mathematics. 2020; 8(12):2221. https://doi.org/10.3390/math8122221

Chicago/Turabian Style

Pfeifer, Dietmar, and Olena Ragulina. 2020. "Adaptive Bernstein Copulas and Risk Management" Mathematics 8, no. 12: 2221. https://doi.org/10.3390/math8122221

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