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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.

Suggested Citation

  • 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," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    2. 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.
    3. Hainaut, Donatien, 2020. "Fractional Hawkes processes," LIDAM Reprints ISBA 2020009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. 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.
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    Cited by:

    1. 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).
    2. Hainaut, Donatien, 2022. "Multivariate claim processes with rough intensities: Properties and estimation," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 269-287.

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