arXiv research

Study optimal dividend and capital injection in insurance portfolios with self-exciting claim arrivals.

A new method for pricing derivatives using self-exciting dynamics and finite-difference transforms.

Optimal reinsurance strategy analyzed for dynamic risk model with self- and externally-excited jumps.

New self-exciting random evolutions (SEREs) for modeling traffic and transport processes.

Paper presents a method for estimating Hawkes process parameters.

Paper analyzes coexisting hidden and self-excited attractors in an economic system.

We provide a general probabilistic framework within which we establish scaling limits for a class of continuous-time stochastic volatility models with self-exciting jump dynamics. In the scaling limit, the joint dynamics of asset returns and volatility is driven by independent Gaussian white noises and two independent …

Paper forecasts financial trading durations using a new point process model.

Develops a goodness-of-fit test for self-exciting processes.

Paper introduces MSPD for multivariate risk processes with dependencies.

This study defines a multivariate Self--Exciting Threshold Autoregressive with eXogenous input (MSETARX) models and present an estimation procedure for the parameters. The conditions for stationarity of the nonlinear MSETARX models is provided. In particular, the efficiency of an adaptive parameter estimation algorithm…

In this paper we studied about the wavelet identification of the thresholds and time delay for more general case without the constraint that the time delay is smaller than the order of the model. Here we composed an empirical wavelet from the SETAR (Self-Exciting Threshold Autoregressive) model and identified the thres…

We consider a self-exciting counting process, the parameters of which depend on a hidden finite-state Markov chain. We derive the optimal filter and smoother for the hidden chain based on observation of the jump process. This filter is in closed form and is finite dimensional. We demonstrate the performance of this fil…

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…

New mechanism found for power laws including Zipf's law.

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 "criticality index" n that quantifies the degree of endogeneity of how much past events tr…

Study analyzes portfolio liquidation games influenced by self-exciting order flow.

Proposes a new jump-diffusion model for option pricing.

The paper models default probabilities and total defaults in credit portfolios using a contagion process with self-exciting jumps.

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…

New model shows negative resilience can improve trading efficiency.

In this paper we consider a mean-field model of interacting diffusions for the monetary reserves in which the reserves are subjected to a self- and cross-exciting shock. This is motivated by the financial acceleration and fire sales observed in the market. We derive a mean-field limit using a weak convergence analysis …

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…

Price changes are induced by aggressive market orders in stock market. We introduce a bivariate marked Hawkes process to model aggressive market order arrivals at the microstructural level. The order arrival intensity is marked by an exogenous part and two endogenous processes reflecting the self-excitation and cross-e…

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…

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…

We introduce and show the existence of a Hawkes self-exciting point process with exponentially-decreasing kernel and where parameters are time-varying. The quantity of interest is defined as the integrated parameter $T^{-1}\int_0^Tθ_t^*dt$, where $θ_t^*$ is the time-varying parameter, and we consider the high-frequency…

Study uses multidimensional SE-NBD process to analyze default portfolios and identify shock amplification.

Develops a new model for multi-currency volatility using CBI-time-changed Lévy processes.

We introduce a new measure of activity of financial markets that provides a direct access to their level of endogeneity. This measure quantifies how much of price changes are due to endogenous feedback processes, as opposed to exogenous news. For this, we calibrate the self-excited conditional Poisson Hawkes model, whi…

Study models market volatility with persistent and temporary impacts.

ARL and Hawkes processes improve market-making strategies with variable volatility.

Paper develops fast, flexible Hawkes process inference for space-time data.

Reinforcement learning improves insurance claims reserving by learning from all claim trajectories.

The study analyzes how bonus-malus systems and delayed claims settlement affect insurance companies' financial stability.

We present simple new examples of pure-jump strict local martingales. The examples are constructed as exponentials of self-exciting affine Markov processes. We characterize the strict local martingale property of these processes by an integral criterion and by non-uniqueness of an associated ordinary differential equat…

A new parallel algorithm speeds up Hawkes process estimation.

Deep Claim predicts payer responses from claims data using deep learning.

New method for individual claims reserving using machine learning.

The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the collective risk model, where the total claim size in a portfolio is the sum of a …

Two machine learning models detect anomalies in ER claims, saving up to 40% in improper payments.

Optimizes insurance processing capacity to minimize costs.

New model bridges pricing and reserving for insurance claims.

This study compares the largest claims from two insurance portfolios using stochastic orderings.

Model detects insurance fraud using social network analysis.

Hawkes processes are a particularly interesting class of stochastic process that have been applied in diverse areas, from earthquake modelling to financial analysis. They are point processes whose defining characteristic is that they 'self-excite', meaning that each arrival increases the rate of future arrivals for som…

We consider trading in a financial market with proportional transaction costs. In the frictionless case, claims are maximal if and only if they are priced by a consistent price process--the equivalent of an equivalent martingale measure. This result fails in the presence of transaction costs. A properly maximal claim i…

Investor maximizes utility from an unknown claim using robust optimization.