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

Dependence Modeling (2016)

• Volume: 4, Issue: 1, page 141-160, electronic only
• ISSN: 2300-2298

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## Abstract

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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.

## How to cite

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Thomas Deschatre. "On the control of the difference between two Brownian motions: a dynamic copula approach." Dependence Modeling 4.1 (2016): 141-160, electronic only. <http://eudml.org/doc/285686>.

@article{ThomasDeschatre2016,
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.},
author = {Thomas Deschatre},
journal = {Dependence Modeling},
keywords = {Brownian motion; Copula; Markovian diffusions; Asymmetric; Difference; Coupling; Risk; copula; asymmetry; coupling; risk},
language = {eng},
number = {1},
pages = {141-160, electronic only},
title = {On the control of the difference between two Brownian motions: a dynamic copula approach},
url = {http://eudml.org/doc/285686},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Thomas Deschatre
TI - On the control of the difference between two Brownian motions: a dynamic copula approach
JO - Dependence Modeling
PY - 2016
VL - 4
IS - 1
SP - 141
EP - 160, electronic only
AB - 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.
LA - eng
KW - Brownian motion; Copula; Markovian diffusions; Asymmetric; Difference; Coupling; Risk; copula; asymmetry; coupling; risk
UR - http://eudml.org/doc/285686
ER -

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