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Thiele's Differential Equation Based on Markov Jump Processes with Non-countable State Space

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  • Emmanuel Coffie
  • Sindre Duedahl
  • Frank Proske

Abstract

In modern life insurance, Markov processes in continuous time on a finite or at least countable state space have been over the years an important tool for the modelling of the states of an insured. Motivated by applications in disability insurance, we propose in this paper a model for insurance states based on Markov jump processes with more general state spaces. We use this model to derive a new type of Thiele's differential equation which e.g. allows for a consistent calculation of reserves in disability insurance based on two-parameter continuous time rehabilitation rates.

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  • Emmanuel Coffie & Sindre Duedahl & Frank Proske, 2021. "Thiele's Differential Equation Based on Markov Jump Processes with Non-countable State Space," Papers 2102.10047, arXiv.org.
    • Handle: RePEc:arx:papers:2102.10047
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    References listed on IDEAS

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    1. Møller,Thomas & Steffensen,Mogens, 2007. "Market-Valuation Methods in Life and Pension Insurance," Cambridge Books, Cambridge University Press, number 9780521868778, October.
    2. Ragnar Norberg, 1995. "A time‐continuous markov chain interest model with applications to insurance," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 11(3), pages 245-256, September.
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