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On Copula-Itô processes

Author

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  • Jaworski Piotr

    (Institute of Mathematics, University of Warsaw, Poland)

Abstract

We study the dynamics of the family of copulas {Ct}t≥0 of a pair of stochastic processes given by stochastic differential equations (SDE). We associate to it a parabolic partial differential equation (PDE). Having embedded the set of bivariate copulas in a dual of a Sobolev Hilbert space H1 (ℝ2)* we calculate the derivative with respect to t and the *weak topology i.e. the tangent vector field to the image of the curve t → Ct. Furthermore we show that the family {Ct}t≥0 is an orbit of a strongly continuous semigroup of transformations and provide the infinitesimal generator of this semigroup.

Suggested Citation

  • Jaworski Piotr, 2019. "On Copula-Itô processes," Dependence Modeling, De Gruyter, vol. 7(1), pages 322-347, January.
    • Handle: RePEc:vrs:demode:v:7:y:2019:i:1:p:322-347:n:17
    DOI: 10.1515/demo-2019-0017
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    References listed on IDEAS

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    1. Enrico Bibbona & Laura Sacerdote & Emiliano Torre, 2016. "A Copula-Based Method to Build Diffusion Models with Prescribed Marginal and Serial Dependence," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 765-783, September.
    2. Jaworski, Piotr & Krzywda, Marcin, 2013. "Coupling of Wiener processes by using copulas," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2027-2033.
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