MEG models for dynamic networks estimate dependencies and shared latent space relationships.
problem Modeling dynamic networks with shared latent space relationships and dependencies.
method MEG combines mutually exciting point processes and latent space models to estimate node-specific parameters and unobserved edges.
result MEG models can estimate intensities for unobserved edges, useful for anomaly detection in real-world applications.
Extends Hawkes process for flexible residual modeling in point processes.
problem Modeling high-frequency financial data with complex residual distributions.
method Introduces self and mutually exciting point process with discretely Markovian dynamics.
result Flexible residual distributions improve intensity modeling and high-frequency data estimation.
A new model predicts network events with improved accuracy and interpretability.
problem Predicting and understanding complex dynamic relational data in networks.
method Mutually Exciting Latent Space Hawkes (LSH) model for continuous-time networks.
result The LSH model outperforms existing models in prediction accuracy and interpretability.
GAttNHP predicts future events in temporal knowledge graphs by encoding long-range dependencies and handling mutual excitation.
problem Forecasting future events in temporal knowledge graphs due to long-range dependencies, mutual excitation, and heavy-tailed inter-arrival times.
method GAttNHP uses a self-attention encoder, semantic soft-grouping, and NCQ regression to address these issues.
result GAttNHP improves entity and time prediction on six benchmark TKG datasets compared to state-of-the-art baselines.
We introduce a Markovian single point process model, with random intensity regulated through a buffer mechanism and a self-exciting effect controlling the arrival stream to the buffer. The model applies the principle of the Hawkes process in which point process jumps generate a shot-noise intensity field. Unlike the Ha…
New CUSUM method detects changes in Hawkes networks efficiently.
problem Detecting abrupt changes in Hawkes networks.
method Efficient online recursive implementation of CUSUM statistic.
result Proposed CUSUM method outperforms existing methods.
We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on linear self and mutually exciting stochastic intensities as introduced by Hawkes. We associ…
Modeling price formation with interacting Hawkes processes leading to stochastic volatility with leverage.
problem Capturing the complex dynamics of price formation in financial markets.
method Agent-based approach to aggregate self-exciting point processes with mean-field interaction.
result Aggregated model converges to a stochastic volatility model with leverage effect and faster-than-linear mean reversion.
It has been suggested that marked point processes might be good candidates for the modelling of financial high-frequency data. A special class of point processes, Hawkes processes, has been the subject of various investigations in the financial community. In this paper, we propose to enhance a basic zero-intelligence o…
Study optimizes investment strategies in markets with contagious price jumps.
problem Optimizing portfolios in financial markets with contagious price jumps.
method Applied stochastic maximum principle, backward stochastic differential equations, and linear-quadratic control techniques.
result Obtained efficient strategy and efficient frontier in semi-closed form.
NNNH uses neural networks to model complex event patterns.
problem Analyzing multi-dimensional nonlinear Hawkes processes with mutual excitation and inhibition.
method NNNH employs feedforward neural networks to model individual kernels and base intensity, optimizing parameters via Stochastic Gradient Descent.
result NNNH accurately captures complexities of nonlinear Hawkes processes, as demonstrated by numerical experiments.
Paper proposes a neural network for non-parametric Hawkes process kernel estimation.
problem Estimating non-parametric Hawkes process kernels efficiently and interpretably.
method Single hidden layer neural network for unbiased log-likelihood estimation of Hawkes processes.
result Proposed neural network achieves comparable or better performance than existing methods.
Targeting a better understanding of credit market dynamics, the authors have studied a stochastic model named the Hawkes process. Describing trades arrival times, this kind of model allows for the capture of self-excitement and mutual interactions phenomena. The authors propose here a simple yet conclusive method for f…
Paper introduces a neural network-based non-stationary influence kernel for complex event data.
problem Modeling complex, non-stationary, and dependent discrete event data.
method Neural Spectral Marked Point Processes (NSMPP) with a versatile non-stationary influence kernel.
result NSMPP outperforms state-of-the-art models on synthetic and real data.
Paper forecasts financial trading durations using a new point process model.
problem Forecasting limit order book durations in high-frequency financial data.
method Self-exciting flexible residual point process incorporating empirical distributional features.
result The model achieves strong predictive performance compared to alternative approaches.
New model for clustering dependent community Hawkes processes in temporal networks.
problem Modeling strong dependence and community structure in temporal networks.
method Dependent Community Hawkes (DCH) models combining stochastic block models and Hawkes processes.
result Spectral clustering error bound derived for DCH models.
Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or impossible to measure the network directly. Examples of latent networks include ec…
Flexible nonlinear Hawkes processes for time-varying systems.
problem Limited expressive ability of classic Hawkes processes.
method Flexible state-switching Hawkes processes with latent variable augmentation for Bayesian inference.
result Superior performance compared to state-of-the-art competitors.
A new model predicts spatio-temporal data using adaptive decision trees and point processes.
problem Predicting spatio-temporal data with real-life applications.
method Hawkes process, adaptive decision tree, joint optimization algorithm.
result Significant improvement in predictions compared to standard methods.
Variational autoencoder models dynamic latent graphs for neural point processes.
problem Modeling event dynamics with changing trends over time.
method Sequential latent variable model with dynamic latent graphs.
result Higher accuracy in predicting inter-event times and event types.
We propose a simulation method for multidimensional Hawkes processes based on superposition theory of point processes. This formulation allows us to design efficient simulations for Hawkes processes with differing exponentially decaying intensities. We demonstrate that inter-arrival times can be decomposed into simpler…
We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate each other with correlated levels of contagion. We generalize a recent algorithm f…
A new metric space model for point process excitations uncovers hidden interactions.
problem Estimating pairwise interactions in multivariate Hawkes processes is often infeasible.
method Developed a Hidden Hawkes Geometry (HHG) model to embed event types in a metric space.
result Learning the embedding reveals salient interactions in various applications.
The Hawkes process is a simple point process, whose intensity function depends on the entire past history and is self-exciting and has the clustering property. The Hawkes process is in general non-Markovian. The linear Hawkes process has immigration-birth representation. Based on that, Fierro et al. recently introduced…
Consider observing a collection of discrete events within a network that reflect how network nodes influence one another. Such data are common in spike trains recorded from biological neural networks, interactions within a social network, and a variety of other settings. Data of this form may be modeled as self-excitin…
Hawkes processes have seen a number of applications in finance, due to their ability to capture event clustering behaviour typically observed in financial systems. Given a calibrated Hawkes process, of concern is the statistical fit to empirical data, particularly for the accurate quantification of self- and mutual-exc…
Model predicts depegging dynamics of stablecoins like Tether and Bitcoin.
problem Understanding depegging effects of stablecoins on cryptocurrencies.
method Multivariate Hawkes process model.
result Numerical example shows model's effectiveness.
Researchers develop methods to learn neuron dynamics from colored noise.
problem Learning nonlocal stochastic neuron dynamics from colored noise.
method Proposed two methods for closing Fokker-Planck equations: nonlocal large-eddy-diffusivity closure and data-driven sparse regression.
result Mutual information and total correlation between stimulus and neuron states calculated for FHN neuron.
Optimal reinsurance strategy analyzed for dynamic risk model with self- and externally-excited jumps.
problem Optimal reinsurance in a dynamic contagion model with self-exciting and externally-exciting risks.
method Two methodologies: classical HJB approach and BSDE approach, focusing on Markovian setting.
result Comparison of self-exciting and externally-exciting risks highlights heightened risk from self-exciting component.
Hawkes processes are a class of simple point processes that are self-exciting and have clustering effect, with wide applications in finance, social networks and many other fields. This paper considers a self-exciting Hawkes process where the baseline intensity is time-dependent, the exciting function is a general funct…
New self-exciting random evolutions (SEREs) for modeling traffic and transport processes.
problem Modeling self-exciting and clustering effects in traffic and transport processes.
method Introducing a new process based on a superposition of a Markov chain and a Hawkes process, and constructing self-exciting random evolutions (SEREs).
result Developed new models and limit theorems for SEREs, including averaging and diffusion approximation.
Develops a goodness-of-fit test for self-exciting processes.
problem Quantifying how well generative models capture self-exciting point processes.
method Connects to Quasi-maximum-likelihood estimator (QMLE) theory and develops a non-parametric self-normalizing statistic, the Generalized Score (GS) statistics.
result Validates the proposed GS test's good performance through numerical simulation and real-data experiments.
A new method for pricing derivatives using self-exciting dynamics and finite-difference transforms.
problem Pricing derivatives with accumulated marks using a self-exciting marked point process.
method Derive discounted pricing equation as a PIDE, transform to one-dimensional PIDEs, use Laplace/Fourier transform, approximate jump term, solve using finite difference scheme.
result Efficiently price derivatives with accumulated marks using a novel finite-difference and transform approach.
New mechanism found for power laws including Zipf's law.
problem Understanding the ubiquity of power law distributions.
method Introduced nonlinear self-excited Hawkes processes with fast-accelerating intensities.
result Wide class of nonlinear Hawkes processes have power law intensity PDFs.
Paper presents a method for estimating Hawkes process parameters.
problem Estimating parameters of Hawkes processes with self-excitation or inhibition.
method Maximum likelihood estimation for Hawkes processes with self-excitation or inhibition.
result The proposed estimator provides more accurate estimations in the inhibition context.
Study optimal dividend and capital injection in insurance portfolios with self-exciting claim arrivals.
problem Optimal dividend and capital injection in insurance portfolios with Hawkes process claim arrivals.
method Analytical properties, explicit threshold, HJB variational inequality, finite-difference scheme, policy-gradient, actor-critic methods.
result Learned strategies closely match the PDE benchmark and remain stable across initial conditions.
Machine learning aids excited-state molecular dynamics studies.
problem Challenges in studying electronically excited states of molecules.
method Employing machine learning techniques for excited-state molecular dynamics.
result Highlight successes and challenges in machine learning for excited-state processes.
We propose a latent self-exciting point process model that describes geographically distributed interactions between pairs of entities. In contrast to most existing approaches that assume fully observable interactions, here we consider a scenario where certain interaction events lack information about participants. Ins…
Modeling high-frequency order book data with Hawkes-Markovian process.
problem Capturing the dynamics of high-frequency order book events.
method Hawkes process with Markovian baseline intensities, LASSO regularization, and Akaike Information Criteria.
result Effective modeling of order book dynamics with reduced parameter redundancy.
Optimal energy trading strategy for intraday markets using Hawkes processes.
problem Optimal execution in intraday energy markets with specific trading patterns.
method Calibrated Hawkes process model with transient price impact.
result Substantial cost reductions in TWAP and VWAP benchmarks.
Improved MLE for Hawkes Processes stabilizes unstable optimization.
problem Unstable Maximum Likelihood Estimation (MLE) for Hawkes Processes.
method Simple stabilization procedure to improve MLE without restrictive assumptions.
result Stabilized MLE outperforms traditional methods over various sequence lengths.
A new model predicts discrete events with flexible, nonparametric baseline and excitation.
problem Limited flexibility in discrete Hawkes models for event prediction.
method Gaussian Process Discrete Hawkes Process (GP-DHP) with collapsed latent representation.
result Improves predictive log-likelihood for diverse event patterns.
The paper models default probabilities and total defaults in credit portfolios using a contagion process with self-exciting jumps.
problem Modeling default probabilities and total defaults in credit portfolios to mitigate credit risk.
method Developed a contagion process with self-exciting jumps to model credit events and derive closed-form expressions for default probabilities and total defaults.
result The proposed framework captures the feedback effect and can be used to price synthetic CDOs.
Multiplex Network Hawkes model for systemic risk measurement
problem Investigate how contagion in financial networks is affected by different transmission channels
method Multiplex Network Hawkes model
result Sparse contagion pathways, with systemic-risk transmission concentrated in outward flows from a small number of influential institutions
We introduce a model-independent approximation for the branching ratio of Hawkes self-exciting point processes. Our estimator requires knowing only the mean and variance of the event count in a sufficiently large time window, statistics that are readily obtained from empirical data. The method we propose greatly simpli…
A new parallel algorithm speeds up Hawkes process estimation.
problem Slow maximum likelihood estimation for Hawkes processes.
method Parallel prefix scan for sparse transition matrices.
result Massive speedup with O(N/P) complexity. We consider the problem of optimal investment and consumption in a class of multidimensional jump-diffusion models in which asset prices are subject to mutually exciting jump processes. This captures a type of contagion where each downward jump in an asset's price results in increased likelihood of further jumps, both …
Paper introduces MSPD for multivariate risk processes with dependencies.
problem Computing risk valuations with dynamic dependencies between frequency and severity.
method Combines Poisson imbedding, pseudo-chaotic expansion, and Malliavin calculus.
result Explicit general correlation formula for MSPDs.