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On Copula-Itô processes

On Copula-Itô processes AbstractWe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Dependence Modeling de Gruyter

On Copula-Itô processes

Jaworski, Piotr
Dependence Modeling , Volume 7 (1): 26 – Jan 1, 2019
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26 pages

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Publisher
de Gruyter
Copyright
© 2019 Piotr Jaworski, published by De Gruyter
ISSN
2300-2298
eISSN
2300-2298
DOI
10.1515/demo-2019-0017
Publisher site
See Article on Publisher Site

Abstract

AbstractWe 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.

Journal

Dependence Modeling – de Gruyter

Published: Jan 1, 2019

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