Risk processes with non-stationary Hawkes claims arrivals

DOI10.1007/s11009-008-9110-6zbMath1231.91239OpenAlexW2165789588MaRDI QIDQ708785

Giovanni Luca Torrisi, Gabriele Stabile

Publication date: 14 October 2010

Published in: Methodology and Computing in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11009-008-9110-6

zbMATH Keywords

importance samplinglarge deviationsHawkes processesPoisson cluster processesruin probabilities

Mathematics Subject Classification ID

Related Items (36)

Locally stationary Hawkes processes ⋮ Optimal dividend policy in an insurance company with contagious arrivals of claims ⋮ RUIN PROBABILITIES FOR A MULTIDIMENSIONAL RISK MODEL WITH NON-STATIONARY ARRIVALS AND SUBEXPONENTIAL CLAIMS ⋮ A dynamic contagion process ⋮ Constant proportion portfolio insurance strategies in contagious markets ⋮ Moments for Hawkes processes with gamma decay kernel functions ⋮ A marked Cox model for the number of IBNR claims: theory ⋮ Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes Jumps ⋮ Limit Theorems for Marked Hawkes Processes with Application to a Risk Model ⋮ A bivariate mutually-excited switching jump diffusion (BMESJD) for asset prices ⋮ Hawkes processes in insurance: risk model, application to empirical data and optimal investment ⋮ Moment generating function of non-Markov self-excited claims processes ⋮ An expansion formula for Hawkes processes and application to cyber-insurance derivatives ⋮ The Cramér-Lundberg model with a fluctuating number of clients ⋮ Process-level large deviations for nonlinear Hawkes point processes ⋮ Optimal reinsurance-investment problem for a general insurance company under a generalized dynamic contagion claim model ⋮ Multivariate Hawkes processes with simultaneous occurrence of excitation events coming from different sources ⋮ Optimal reinsurance via BSDEs in a partially observable model with jump clusters ⋮ Diffusion approximation of a risk model with non-stationary Hawkes arrivals of claims ⋮ Moderate deviations for a Hawkes-type risk model with arbitrary dependence between claim sizes and waiting times ⋮ A GENERALIZED CONTAGION PROCESS WITH AN APPLICATION TO CREDIT RISK ⋮ Large deviations and applications for Markovian Hawkes processes with a large initial intensity ⋮ Transform approach for discounted aggregate claims in a risk model with descendant claims ⋮ Asymptotic analysis for affine point processes with large initial intensity ⋮ Precise deviations for Hawkes processes ⋮ Ruin by dynamic contagion claims ⋮ Limit theorems for non-Markovian marked dynamic contagion processes ⋮ A bivariate shot noise self-exciting process for insurance ⋮ Ruin probabilities for risk processes with non-stationary arrivals and subexponential claims ⋮ Functional limit theorems for marked Hawkes point measures ⋮ On the total claim amount for marked Poisson cluster models ⋮ Large Deviation Results for Wave Governed Random Motions Driven by Semi-Markov Processes ⋮ Optimal reinsurance-investment strategy for a dynamic contagion claim model ⋮ Hedging strategy for unit-linked life insurance contracts with self-exciting jump clustering ⋮ Large deviations for Markovian nonlinear Hawkes processes ⋮ Approximations for finite-time ruin probability in a dependent discrete-time risk model with CMC simulations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Importance sampling in the Monte Carlo study of sequential tests
• Big queues.
• Stability results for a general class of interacting point processes dynamics, and applications
• Simple approximations of ruin probabilities
• Explosive Poisson shot noise processes with applications to risk reserves
• Stability of nonlinear Hawkes processes
• Rate of convergence to equilibrium of marked Hawkes processes
• A class of interacting marked point processes: rate of convergence to equilibrium
• Ruin probabilities and aggregrate claims distributions for shot noise Cox processes
• Large Deviations of Poisson Cluster Processes
• Simulating level-crossing probabilities by importance sampling
• A cluster process representation of a self-exciting process
• An insensitivity property of Lundberg's estimate for delayed claims
• An Introduction to the Theory of Point Processes
• Large deviations and overflow probabilities for the general single-server queue, with applications
• A class of risk processes with delayed claims: ruin probability estimates under heavy tail conditions
• Spectra of some self-exciting and mutually exciting point processes
• Estimating value-at-risk: a point process approach

This page was built for publication: Risk processes with non-stationary Hawkes claims arrivals