Ergodicity and scaling limit of a constrained multivariate Hawkes process

Ban Zheng (), François Roueff () and Frédéric Abergel ()
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Ban Zheng: FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec, LTCI - Laboratoire Traitement et Communication de l'Information - Télécom ParisTech - IMT - Institut Mines-Télécom [Paris] - CNRS - Centre National de la Recherche Scientifique
François Roueff: LTCI - Laboratoire Traitement et Communication de l'Information - Télécom ParisTech - IMT - Institut Mines-Télécom [Paris] - CNRS - Centre National de la Recherche Scientifique
Frédéric Abergel: FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec, MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris

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Abstract: 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.

Keywords: Point processes; Hawkes processes; Limit theorems; Discretisation of stochastic processes; limit order book (search for similar items in EconPapers)
Date: 2014-02-04
New Economics Papers: this item is included in nep-mst
Note: View the original document on HAL open archive server: https://hal.science/hal-00777941v2
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Citations: View citations in EconPapers (8)

Published in SIAM Journal on Financial Mathematics, 2014, 5 (1), pp.P. 99-136. ⟨10.1137/130912980⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00777941

DOI: 10.1137/130912980

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