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This work contributes to the theory and applications of Hawkes processes. We introduce and examine a new class of Hawkes processes that we call generalized Hawkes processes, and their special subclass -- the generalized multivariate Hawkes…
We propose a general non-linear order book model that is built from the individual behaviours of the agents. Our framework encompasses Markovian and Hawkes based models. Under mild assumptions, we prove original results on the ergodicity…
Procurement in maritime logistics faces challenges due to uncertainties in demand and fluctuating market conditions. To address these complexities, we introduce a flexible discrete-event simulation framework that models the request-to-order…
Previous work has shown that popular trending events are important external factors which pose significant influence on user search behavior and also provided a way to computationally model this influence. However, their problem formulation…
We give functional laws of large numbers for a class of marked Hawkes processes and marked compound Hawkes processes with a general mark space. Our results provide some complement to those presented previously in the literature. As an…
Recommender systems are central to modern online platforms, but a popular concern is that they may be pulling society in dangerous directions (e.g., towards filter bubbles). However, a challenge with measuring the effects of recommender…
To operate process engineering systems in a safe and reliable manner, predictive models are often used in decision making. In many cases, these are mechanistic first principles models which aim to accurately describe the process. In…
We present a graphical and dynamic framework for binding and execution of business) process models. It is tailored to integrate 1) ad hoc processes modeled graphically, 2) third party services discovered in the (Inter)net, and 3)…
The multivariate Hawkes process is a past-dependent point process used to model the relationship of event occurrences between different phenomena.Although the Hawkes process was originally introduced to describe excitation effects, which…
We consider a 2-dimensional marked Hawkes process with increasing baseline intensity in order to model prices on electricity intraday markets. This model allows to represent different empirical facts such as increasing market activity,…
Nowadays there is a large availability of discrete event simulation software that can be easily used in different domains: from industry to supply chain, from healthcare to business management, from training to complex systems design.…
We generalise the construction of multivariate Hawkes processes to a possibly infinite network of counting processes on a directed graph $\mathbb G$. The process is constructed as the solution to a system of Poisson driven stochastic…
Hawkes process provides an effective statistical framework for analyzing the time-dependent interaction of neuronal spiking activities. Although utilized in many real applications, the classic Hawkes process is incapable of modelling…
Hawkes processes are often applied to model dependence and interaction phenomena in multivariate event data sets, such as neuronal spike trains, social interactions, and financial transactions. In the nonparametric setting, learning the…
The neural Hawkes process (Mei & Eisner, 2017) is a generative model of irregularly spaced sequences of discrete events. To handle complex domains with many event types, Mei et al. (2020a) further consider a setting in which each event in…
This paper uses the development of multi-agent market models to present a unified approach to the joint questions of how financial market movements may be simulated, predicted, and hedged against. We examine the effect of different market…
We present a careful analysis of possible issues on the application of the self-excited Hawkes process to high-frequency financial data. We carefully analyze a set of effects leading to significant biases in the estimation of the…
In this paper, we study various new Hawkes processes, namely, so-called general compound and regime-switching general compound Hawkes processes to model the price processes in the limit order books. We prove Law of Large Numbers (LLN) and…
Hawkes processes are a self-exciting stochastic process used to describe phenomena whereby past events increase the probability of the occurrence of future events. This work presents a flexible approach for modelling a variant of these,…
In this study, we developed a computational framework for simulating large-scale agent-based financial markets. Our platform supports trading multiple simultaneous assets and leverages distributed computing to scale the number and…