Diffusion Approximation of a Risk Model with Non-Stationary Hawkes Arrivals of Claims

Cheng, Zailei; Seol, Youngsoo

doi:10.1007/s11009-019-09722-8

Cited by 8 publications

(1 citation statement)

References 29 publications

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“…Hawkes Processes for Insurance Since recently, insurance companies are developing an interest for Hawkes processes. They are used for calculating Solvency Capital Requirements and modelling different indicators of risks, such as ruin (improvement of Cramer-Lundberg model, see Cheng and Seol (2020)) or cyber-attacks (see Bessy-Roland et al (2020)). Hawkes processes model claims arrival, considered to follow a Poisson process in classic approaches.…”

Section: Discussionmentioning

confidence: 99%

Hawkes Processes Framework With a Gamma Density As Excitation Function: Application to Natural Disasters for Insurance

Lesage

Deaconu

Lejay

et al. 2022

Methodol Comput Appl Probab

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Hawkes processes are temporal self-exciting point processes. They are well established in earthquake modelling or finance and their application is spreading to diverse areas. Most models from the literature have two major drawbacks regarding their potential application to insurance. First, they use an exponentially-decaying form of excitation, which does not allow a delay between the occurrence of an event and its excitation effect on the process and does not fit well on insurance data consequently. Second, theoretical results developed from these models are valid only when time of observation tends to infinity, whereas the time horizon for an insurance use case is of several months or years. In this paper, we define a complete framework of Hawkes processes with a Gamma density excitation function (i.e. estimation, simulation, goodness-of-fit) instead of an exponential-decaying function and we demonstrate some mathematical properties (i.e. expectation, variance) about the transient regime of the process. We illustrate our results with real insurance data about natural disasters in Luxembourg.

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Section: Discussionmentioning

confidence: 99%