A spatial Markov-modulated marked Hawkes process for parametric insurance

Donatien Hainaut ()
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Donatien Hainaut: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2026036, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: This paper introduces a tractable Markov-modulated marked Hawkes process for modelling spatial clustered events and pricing parametric insurance. The model combines spatial self-excitation, event-specific marks and a latent continuous-time Markov chain whose state, updated at event times, governs the intensity, triggering mechanism and mark distribution. This specification preserves regime-switching dynamics while simplifying likelihood evaluation. We derive the likelihood of the observed process and develop forward-backward filtering and an expectation maximization (EM) algorithm for estimating the model when the regimes are unobserved. We also establish a sufficient stability condition and provide a simulation procedure for generating event times, locations, marks and latent regimes. The framework is applied to earthquake data from Greece using a switching Epidemic Type Aftershock Sequence (ETAS) model with Pareto-distributed magnitudes. The empirical analysis shows that the model captures temporal clustering and alternating periods of seismic activity, while reproducing the central tendency of earthquake magnitudes. Finally, we apply the model to price a regional parametric earthquake insurance contract covering an elliptical area around Athens. These results illustrate how latent regime switching, spatial dependence and event severity can be jointly incorporated into catastrophe risk modelling and parametric insurance pricing.

Keywords: Hawkes process; Markov-modulated process; spatial process; parametric insurance (search for similar items in EconPapers)
Pages: 31
Date: 2026-10-20
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvad:2026036

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