On the control of the difference between two Brownian motions: a dynamic copula approach

Deschatre Thomas
Additional contact information
Deschatre Thomas: CEREMADE, Université Paris-Dauphine, Place du maréchal De Lattre de Tassigny 75775 Paris Cedex 16, France

Dependence Modeling, 2016, vol. 4, issue 1, 20

Abstract: We propose new copulae to model the dependence between two Brownian motions and to control the distribution of their difference. Our approach is based on the copula between the Brownian motion and its reflection. We show that the class of admissible copulae for the Brownian motions are not limited to the class of Gaussian copulae and that it also contains asymmetric copulae. These copulae allow for the survival function of the difference between two Brownian motions to have higher value in the right tail than in the Gaussian copula case. Considering two Brownian motions B1t and B2t, the main result is that the range of possible values for is the same for Markovian pairs and all pairs of Brownian motions, that is with φ being the cumulative distribution function of a standard Gaussian random variable.

Keywords: Brownian motion; Copula; Markovian diffusions; Asymmetric; Difference; Coupling; Risk (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/demo-2016-0007 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:4:y:2016:i:1:p:141-160:n:7

DOI: 10.1515/demo-2016-0007

Access Statistics for this article

Dependence Modeling is currently edited by Giovanni Puccetti

More articles in Dependence Modeling from De Gruyter
Bibliographic data for series maintained by Peter Golla ().