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This article presents a Hawkes process model with Markovian baseline intensities for high-frequency order book data modeling. We classify intraday order book trading events into a range of categories based on their order types and the price…

Trading and Market Microstructure · Quantitative Finance 2022-01-07 Philip Protter , Qianfan Wu , Shihao Yang

In this paper, a framework on a discrete observation of (marked) point processes under the high-frequency observation is developed. Based on this framework, we first clarify the relation between random coefficient integer-valued…

Statistics Theory · Mathematics 2017-04-11 Daisuke Kurisu

The present paper provides exact mathematical expressions for the high-order moments of spiking activity in a recurrently-connected network of linear Hawkes processes. It extends previous studies that have explored the case of a (linear)…

Neurons and Cognition · Quantitative Biology 2019-12-17 Matthieu Gilson , Jean-Pascal Pfister

We study a linear price impact model including other liquidity takers, whose flow of orders either follows a Poisson or a Hawkes process. The optimal execution problem is solved explicitly in this context, and the closed-formula optimal…

Trading and Market Microstructure · Quantitative Finance 2015-06-10 Aurélien Alfonsi , Pierre Blanc

We study finite horizon optimal switching problems for hidden Markov chain models under partially observable Poisson processes. The controller possesses a finite range of strategies and attempts to track the state of the unobserved state…

Optimization and Control · Mathematics 2008-05-22 Erhan Bayraktar , Mike Ludkovski

The Hawkes process and its extensions effectively model self-excitatory phenomena including earthquakes, viral pandemics, financial transactions, neural spike trains and the spread of memes through social networks. The usefulness of these…

Applications · Statistics 2020-05-21 Andrew J. Holbrook , Charles E. Loeffler , Seth R. Flaxman , Marc A. Suchard

Asynchronous events on the continuous time domain, e.g., social media actions and stock transactions, occur frequently in the world. The ability to recognize occurrence patterns of event sequences is crucial to predict which typeof events…

Machine Learning · Computer Science 2020-02-17 Qiang Zhang , Aldo Lipani , Omer Kirnap , Emine Yilmaz

In this paper, we introduce a suite of models for price-aware automated market making platforms willing to optimize their quotes. These models incorporate advanced price dynamics, including stochastic volatility, jumps, and microstructural…

Trading and Market Microstructure · Quantitative Finance 2024-05-21 Philippe Bergault , Louis Bertucci , David Bouba , Olivier Guéant , Julien Guilbert

This paper presents a method for forecasting limit order book durations using a self-exciting flexible residual point process. High-frequency events in modern exchanges exhibit heavy-tailed interarrival times, posing a significant challenge…

Statistical Finance · Quantitative Finance 2026-04-02 Kyungsub Lee

This study examines the use of a recurrent neural network for estimating the parameters of a Hawkes model based on high-frequency financial data, and subsequently, for computing volatility. Neural networks have shown promising results in…

Statistical Finance · Quantitative Finance 2023-04-25 Kyungsub Lee

Modelling and forecasting the occurrence of extreme events is especially difficult when the event process is nonstationary, with changes in both the rate at which extremes occur and the magnitude of the extremes when they occur. We approach…

Methodology · Statistics 2026-05-06 Gordon J. Ross , Dean Markwick

A Hawkes process model with a time-varying background rate is developed for analyzing the high-frequency financial data. In our model, the logarithm of the background rate is modeled by a linear model with a relatively large number of…

Statistical Finance · Quantitative Finance 2017-07-24 Takahiro Omi , Yoshito Hirata , Kazuyuki Aihara

Critically ill patients in regular wards are vulnerable to unanticipated adverse events which require prompt transfer to the intensive care unit (ICU). To allow for accurate prognosis of deteriorating patients, we develop a novel…

Machine Learning · Computer Science 2017-05-16 Ahmed M. Alaa , Scott Hu , Mihaela van der Schaar

Recently proposed encoder-decoder structures for modeling Hawkes processes use transformer-inspired architectures, which encode the history of events via embeddings and self-attention mechanisms. These models deliver better prediction and…

Machine Learning · Computer Science 2022-02-07 Yamac Alican Isik , Connor Davis , Paidamoyo Chapfuwa , Ricardo Henao

Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to…

Machine Learning · Computer Science 2021-06-10 Feng Zhou , Quyu Kong , Yixuan Zhang , Cheng Feng , Jun Zhu

The Hawkes process (HP) is commonly used to model event sequences with self-reinforcing dynamics, including electronic health records (EHRs). Traditional HPs capture self-reinforcement via parametric impact functions that can be inspected…

Machine Learning · Statistics 2025-10-23 Yuankang Zhao , Matthew Engelhard

A simple Hawkes model have been developed for the price tick structure dynamics incorporating market microstructure noise and trade clustering. In this paper, the model is extended with random mark to deal with more realistic price tick…

Statistical Finance · Quantitative Finance 2019-07-30 Kyungsub Lee , Byoung Ki Seo

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…

Applications · Statistics 2014-02-14 Ban Zheng , François Roueff , Frédéric Abergel

The primary objective of this paper is to conceive and develop a new methodology to detect notable changes in liquidity within an order-driven market. We study a market liquidity model which allows us to dynamically quantify the level of…

Mathematical Finance · Quantitative Finance 2023-10-16 Etienne Chevalier , Yadh Hafsi , Vathana Ly Vath

We propose a novel modeling framework for time-evolving networks allowing for long-term dependence in network features that update in continuous time. Dynamic network growth is functionally parameterized via the conditional intensity of a…

Methodology · Statistics 2026-03-20 Duncan A Clark , Conor J. Kresin , Charlotte M. Jones-Todd