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A fractional multi-states model for insurance

Author

Listed:
  • Hainaut, Donatien

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

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," LIDAM Reprints ISBA 2021014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2021014
    DOI: https://doi.org/10.1016/j.insmatheco.2021.02.004
    Note: In: Insurance: Mathematics and Economics, Vol. 98, p. 120-132 (2021)
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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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