Estimation of the parameters of a Markov-modulated loss process in insurance

Armelle Guillou (), Stéphane Loisel () and Gilles Stupfler
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Armelle Guillou: IRMA - Institut de Recherche Mathématique Avancée - UNISTRA - Université de Strasbourg - CNRS - Centre National de la Recherche Scientifique
Stéphane Loisel: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon

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Abstract: We present a new model of loss processes in insurance. The process is a couple $(N, \, L)$ where $N$ is a univariate Markov-modulated Poisson process (MMPP) and $L$ is a multivariate loss process whose behaviour is driven by $N$. We prove the strong consistency of the maximum likelihood estimator of the parameters of this model, and present an EM algorithm to compute it in practice. The method is illustrated with simulations and real sets of insurance data.

Date: 2013
Note: View the original document on HAL open archive server: https://hal.science/hal-00589696v1
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Citations: View citations in EconPapers (6)

Published in Insurance: Mathematics and Economics, 2013, 53, pp.388-404. ⟨10.1016/j.insmatheco.2013.07.003⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00589696

DOI: 10.1016/j.insmatheco.2013.07.003

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