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

• Autorzy: Thomas Deschatre
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Brownian motion; Copula; Markovian diffusions; Asymmetric; Difference; Coupling; Risk

• Wydawca: De Gruyter Open
• Czasopismo: Dependence Modeling
• Rocznik: 2016
• Tom: 4
• Numer: 1

Daty

otrzymano

2016-01-20

zaakceptowano

2016-07-04

online

2016-07-28

Twórcy

autor

Thomas Deschatre

• CEREMADE, Université Paris-Dauphine, Place du maréchal De Lattre de Tassigny 75775 Paris Cedex 16, France

Identyfikatory

DOI

10.1515/demo-2016-0007