An expansion formula for Hawkes processes and application to cyber-insurance derivatives

DOI10.1016/j.spa.2023.02.012zbMath1511.60071arXiv2104.01579OpenAlexW3152048755MaRDI QIDQ6044248

Mathieu Rosenbaum, Anthony Réveillac, Caroline Hillairet

Publication date: 17 May 2023

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.01579

zbMATH Keywords

Malliavin calculusHawkes processpricing formulaecyber insurance derivatives

Mathematics Subject Classification ID

Stochastic calculus of variations and the Malliavin calculus (60H07) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Actuarial mathematics (91G05)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Structural credit risk modelling with Hawkes jump diffusion processes
• Gaussian approximation of nonlinear Hawkes processes
• Risk processes with non-stationary Hawkes claims arrivals
• Approximations for stop-loss reinsurance premiums
• Some non asymptotic tail estimates for Hawkes processes
• On the numerical evaluation of the distribution of aggregate claims and its stop-loss premiums
• An introduction to the theory of point processes
• Stop-loss premiums under dependence
• Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity
• Large deviations and applications for Markovian Hawkes processes with a large initial intensity
• Duality formulas on the Poisson space
• A bivariate shot noise self-exciting process for insurance
• Recursive computation of the Hawkes cumulants
• Pricing formulae for derivatives in insurance using Malliavin calculus
• Ruin by dynamic contagion claims
• Some limit theorems for Hawkes processes and application to financial statistics
• Stability of nonlinear Hawkes processes
• Dependent risks and excess of loss reinsurance
• A GENERALIZED CONTAGION PROCESS WITH AN APPLICATION TO CREDIT RISK
• Affine Point Processes and Portfolio Credit Risk
• An elementary derivation of moments of Hawkes processes
• On Lewis' simulation method for point processes
• Transform analysis for Hawkes processes with applications in dark pool trading
• Renewal in Hawkes processes with self-excitation and inhibition
• Modeling and predicting extreme cyber attack rates via marked point processes
• Spectra of some self-exciting and mutually exciting point processes

This page was built for publication: An expansion formula for Hawkes processes and application to cyber-insurance derivatives