Ergodicity and scaling limit of a constrained multivariate Hawkes process - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Financial Mathematics Année : 2014

Ergodicity and scaling limit of a constrained multivariate Hawkes process

Résumé

We introduce a multivariate Hawkes process with constraints on its conditional density. It is a multivariate point process with conditional intensity similar to that of a multivariate Hawkes process but certain events are forbidden with respect to boundary conditions on a multidimensional constraint variable, whose evolution is driven by the point process. We study this process in the special case where the fertility function is exponential so that the process is entirely described by an underlying Markov chain, which includes the constraint variable. Some conditions on the parameters are established to ensure the ergodicity of the chain. Moreover, scaling limits are derived for the integrated point process. This study is primarily motivated by the stochastic modelling of a limit order book for high frequency financial data analysis.
Fichier principal
Vignette du fichier
const-hawkes-sifin.pdf (661.16 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00777941 , version 1 (18-01-2013)
hal-00777941 , version 2 (13-02-2014)

Identifiants

Citer

Ban Zheng, François Roueff, Frédéric Abergel. Ergodicity and scaling limit of a constrained multivariate Hawkes process. SIAM Journal on Financial Mathematics, 2014, 5 (1), pp.P. 99-136. ⟨10.1137/130912980⟩. ⟨hal-00777941v2⟩
474 Consultations
434 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More