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A fractional multi-states model for insurance

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  • Hainaut, Donatien

Abstract

A common approach for pricing insurance contracts consists to represent the insured’s health status by a Markov chain. This article extends this framework by observing this chain on a random scale of time, defined as the inverse of an α-stable process. This stochastic clock induces sub-exponential waiting times spent in each state. We first review and extend the properties of this time-change to a conditional filtration at time t>0. Next we evaluate a general type of insurance contract from inception to expiry.

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  • Hainaut, Donatien, 2021. "A fractional multi-states model for insurance," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 120-132.
    • Handle: RePEc:eee:insuma:v:98:y:2021:i:c:p:120-132
    DOI: 10.1016/j.insmatheco.2021.02.004
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    References listed on IDEAS

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    1. Hainaut, Donatien, 2020. "Fractional Hawkes processes," LIDAM Reprints ISBA 2020009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Hainaut, Donatien, 2020. "Fractional Hawkes processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    3. Piryatinska, A. & Saichev, A.I. & Woyczynski, W.A., 2005. "Models of anomalous diffusion: the subdiffusive case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 375-420.
    4. D'Amico, Guglielmo & Guillen, Montserrat & Manca, Raimondo, 2009. "Full backward non-homogeneous semi-Markov processes for disability insurance models: A Catalunya real data application," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 173-179, October.
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    Cited by:

    1. Hainaut, Donatien, 2022. "Multivariate claim processes with rough intensities: Properties and estimation," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 269-287.
    2. Yoshioka, Hidekazu, 2025. "Superposition of interacting stochastic processes with memory and its application to migrating fish counts," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    3. Dupret, Jean-Loup & Hainaut, Donatien, 2022. "A subdiffusive stochastic volatility jump model," LIDAM Discussion Papers ISBA 2022001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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