On Copula-Itô processes

Jaworski Piotr ()
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Jaworski Piotr: Institute of Mathematics, University of Warsaw, Poland

Dependence Modeling, 2019, vol. 7, issue 1, 322-347

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.

Keywords: Copulas; copula processes; stochastic differential equations; parabolic partial differential equations; semigroups of transformations (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:7:y:2019:i:1:p:322-347:n:17

DOI: 10.1515/demo-2019-0017

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