An expansion formula for Hawkes processes and application to cyber-insurance derivatives * - INSA Toulouse - Institut National des Sciences Appliquées de Toulouse Access content directly
Preprints, Working Papers, ... Year : 2021

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

Abstract

In this paper we provide an expansion formula for Hawkes processes which involves the addition of jumps at deterministic times to the Hawkes process in the spirit of the wellknown integration by parts formula (or more precisely the Mecke formula) for Poisson functional. Our approach allows us to provide an expansion of the premium of a class of cyber insurance derivatives (such as reinsurance contracts including generalized Stop-Loss contracts) or risk management instruments (like Expected Shortfall) in terms of so-called shifted Hawkes processes. From the actuarial point of view, these processes can be seen as "stressed" scenarios. Our expansion formula for Hawkes processes enables us to provide lower and upper bounds on the premium (or the risk evaluation) of such cyber contracts and to quantify the surplus of premium compared to the standard modeling with a homogenous Poisson process.
Fichier principal
Vignette du fichier
Hillairet_Reveillac_Rosenbaum.pdf (532.73 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03189601 , version 1 (04-04-2021)

Identifiers

  • HAL Id : hal-03189601 , version 1

Cite

Caroline Hillairet, Anthony Réveillac, Mathieu Rosenbaum. An expansion formula for Hawkes processes and application to cyber-insurance derivatives *. 2021. ⟨hal-03189601⟩
169 View
257 Download

Share

Gmail Mastodon Facebook X LinkedIn More