Aggregate Markov models in life insurance: Properties and valuation

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Aggregate Markov models in life insurance: Properties and valuation. / Ahmad, Jamaal; Bladt, Mogens; Furrer, Christian.

I: Insurance: Mathematics and Economics, Bind 113, 2023, s. 50-69.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Ahmad, J, Bladt, M & Furrer, C 2023, 'Aggregate Markov models in life insurance: Properties and valuation', Insurance: Mathematics and Economics, bind 113, s. 50-69. https://doi.org/10.1016/j.insmatheco.2023.07.006

APA

Ahmad, J., Bladt, M., & Furrer, C. (2023). Aggregate Markov models in life insurance: Properties and valuation. Insurance: Mathematics and Economics, 113, 50-69. https://doi.org/10.1016/j.insmatheco.2023.07.006

Vancouver

Ahmad J, Bladt M, Furrer C. Aggregate Markov models in life insurance: Properties and valuation. Insurance: Mathematics and Economics. 2023;113:50-69. https://doi.org/10.1016/j.insmatheco.2023.07.006

Author

Ahmad, Jamaal ; Bladt, Mogens ; Furrer, Christian. / Aggregate Markov models in life insurance: Properties and valuation. I: Insurance: Mathematics and Economics. 2023 ; Bind 113. s. 50-69.

Bibtex

@article{f98a07de8ccd4adb8c03c9e3a8cf70eb,
title = "Aggregate Markov models in life insurance: Properties and valuation",
abstract = "In multi-state life insurance, an adequate balance between analytic tractability, computational efficiency, and statistical flexibility is of great importance. This might explain the popularity of Markov chain modelling, where matrix analytic methods allow for a comprehensive treatment. Unfortunately, Markov chain modelling is unable to capture duration effects, so this paper presents aggregate Markov models as an alternative. Aggregate Markov models retain most of the analytical tractability of Markov chains, yet are non-Markovian and thus more flexible. Based on an explicit characterization of the fundamental martingales, matrix representations of the expected accumulated cash flows and corresponding prospective reserves are derived for duration-dependent payments with and without incidental policyholder behaviour. Throughout, special attention is given to a semi-Markovian case. Finally, the methods and results are illustrated in a numerical example.",
author = "Jamaal Ahmad and Mogens Bladt and Christian Furrer",
year = "2023",
doi = "10.1016/j.insmatheco.2023.07.006",
language = "English",
volume = "113",
pages = "50--69",
journal = "Insurance: Mathematics and Economics",
issn = "0167-6687",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Aggregate Markov models in life insurance: Properties and valuation

AU - Ahmad, Jamaal

AU - Bladt, Mogens

AU - Furrer, Christian

PY - 2023

Y1 - 2023

N2 - In multi-state life insurance, an adequate balance between analytic tractability, computational efficiency, and statistical flexibility is of great importance. This might explain the popularity of Markov chain modelling, where matrix analytic methods allow for a comprehensive treatment. Unfortunately, Markov chain modelling is unable to capture duration effects, so this paper presents aggregate Markov models as an alternative. Aggregate Markov models retain most of the analytical tractability of Markov chains, yet are non-Markovian and thus more flexible. Based on an explicit characterization of the fundamental martingales, matrix representations of the expected accumulated cash flows and corresponding prospective reserves are derived for duration-dependent payments with and without incidental policyholder behaviour. Throughout, special attention is given to a semi-Markovian case. Finally, the methods and results are illustrated in a numerical example.

AB - In multi-state life insurance, an adequate balance between analytic tractability, computational efficiency, and statistical flexibility is of great importance. This might explain the popularity of Markov chain modelling, where matrix analytic methods allow for a comprehensive treatment. Unfortunately, Markov chain modelling is unable to capture duration effects, so this paper presents aggregate Markov models as an alternative. Aggregate Markov models retain most of the analytical tractability of Markov chains, yet are non-Markovian and thus more flexible. Based on an explicit characterization of the fundamental martingales, matrix representations of the expected accumulated cash flows and corresponding prospective reserves are derived for duration-dependent payments with and without incidental policyholder behaviour. Throughout, special attention is given to a semi-Markovian case. Finally, the methods and results are illustrated in a numerical example.

U2 - 10.1016/j.insmatheco.2023.07.006

DO - 10.1016/j.insmatheco.2023.07.006

M3 - Journal article

VL - 113

SP - 50

EP - 69

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

SN - 0167-6687

ER -

ID: 365879388