Hawkes processes framework with a Gamma density as excitation function: application to natural disasters for insurance

Laurent Lesage (), Madalina Deaconu (), Antoine Lejay (), Jorge Meira, Geoffrey Nichil and Radu State
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Laurent Lesage: IECL - Institut Élie Cartan de Lorraine - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique, SnT - Interdisciplinary Centre for Security, Reliability and Trust [Luxembourg] - uni.lu - Université du Luxembourg = University of Luxembourg = Universität Luxemburg, Foyer Assurances [Leudelange], PASTA - Processus aléatoires spatio-temporels et leurs applications - Centre Inria de l'Université de Lorraine - Inria - Institut National de Recherche en Informatique et en Automatique - IECL - Institut Élie Cartan de Lorraine - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique
Madalina Deaconu: IECL - Institut Élie Cartan de Lorraine - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique, PASTA - Processus aléatoires spatio-temporels et leurs applications - Centre Inria de l'Université de Lorraine - Inria - Institut National de Recherche en Informatique et en Automatique - IECL - Institut Élie Cartan de Lorraine - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique
Antoine Lejay: IECL - Institut Élie Cartan de Lorraine - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique, PASTA - Processus aléatoires spatio-temporels et leurs applications - Centre Inria de l'Université de Lorraine - Inria - Institut National de Recherche en Informatique et en Automatique - IECL - Institut Élie Cartan de Lorraine - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique
Jorge Meira: SnT - Interdisciplinary Centre for Security, Reliability and Trust [Luxembourg] - uni.lu - Université du Luxembourg = University of Luxembourg = Universität Luxemburg
Geoffrey Nichil: Foyer Assurances [Leudelange]
Radu State: SnT - Interdisciplinary Centre for Security, Reliability and Trust [Luxembourg] - uni.lu - Université du Luxembourg = University of Luxembourg = Universität Luxemburg

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Abstract: Hawkes process 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: 2022-03-05
New Economics Papers: this item is included in nep-rmg
Note: View the original document on HAL open archive server: https://inria.hal.science/hal-03040090v1
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Citations: View citations in EconPapers (2)

Published in Methodology and Computing in Applied Probability, 2022, pp.29. ⟨10.1007/s11009-022-09938-1⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03040090

DOI: 10.1007/s11009-022-09938-1

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