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

Laurent Lesage (), Madalina Deaconu, Antoine Lejay, Jorge Augusto Meira, Geoffrey Nichil and Radu State
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Laurent Lesage: University of Lorraine, CNRS, Inria, IECL
Madalina Deaconu: University of Lorraine, CNRS, Inria, IECL
Antoine Lejay: University of Lorraine, CNRS, Inria, IECL
Jorge Augusto Meira: University of Luxembourg
Geoffrey Nichil: Foyer Assurances
Radu State: University of Luxembourg

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 4, 2509-2537

Abstract: Abstract 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.

Keywords: Point processes; Hawkes processes; Insurance; EM algorithm; Natural disasters (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-022-09938-1

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