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Modelling and simulation of dependence structures in nonlife insurance with Bernstein copulas

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  • Dietmar Pfeifer
  • Doreen Strassburger
  • Joerg Philipps

Abstract

In this paper we review Bernstein and grid-type copulas for arbitrary dimensions and general grid resolutions in connection with discrete random vectors possessing uniform margins. We further suggest a pragmatic way to fit the dependence structure of multivariate data to Bernstein copulas via grid-type copulas and empirical contingency tables. Finally, we discuss a Monte Carlo study for the simulation and PML estimation for aggregate dependent losses form observed windstorm and flooding data.

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  • Dietmar Pfeifer & Doreen Strassburger & Joerg Philipps, 2020. "Modelling and simulation of dependence structures in nonlife insurance with Bernstein copulas," Papers 2010.15709, arXiv.org.
    • Handle: RePEc:arx:papers:2010.15709
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    References listed on IDEAS

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    1. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V.K. & TAAMOUTI, Abderrahim, 2008. "Asymptotic properties of the Bernstein density copula for dependent data," LIDAM Discussion Papers CORE 2008045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Tomasz Kulpa, 1999. "On approximation of copulas," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 22, pages 1-11, January.
    3. Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(3), pages 535-562, June.
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