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Disability insurance with collective health claims: A mean-field approach

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  • Christian Furrer
  • Philipp C. Hornung

Abstract

The classic semi-Markov disability model is expanded with individual and collective health claims to improve its explanatory and predictive power -- in particular in the context of group experience rating. The inclusion of collective health claims leads to a computationally challenging many-body problem. By adopting a mean-field approach, this many-body problem can be approximated by a non-linear one-body problem, which in turn leads to a transparent pricing method for disability coverages based on a lower-dimensional system of non-linear forward integro-differential equations. In a practice-oriented simulation study, the mean-field approximation clearly stands its ground in comparison to na\"ive Monte Carlo methods.

Suggested Citation

  • Christian Furrer & Philipp C. Hornung, 2025. "Disability insurance with collective health claims: A mean-field approach," Papers 2512.13562, arXiv.org.
    • Handle: RePEc:arx:papers:2512.13562
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    References listed on IDEAS

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    3. Kristian Buchardt & Thomas Møller & Kristian Bjerre Schmidt, 2015. "Cash flows and policyholder behaviour in the semi-Markov life insurance setup," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2015(8), pages 660-688, November.
    4. Eugene Feinberg & Manasa Mandava & Albert N. Shiryaev, 2022. "Kolmogorov’s equations for jump Markov processes with unbounded jump rates," Annals of Operations Research, Springer, vol. 317(2), pages 587-604, October.
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