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A time‐continuous markov chain interest model with applications to insurance

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  • Ragnar Norberg

Abstract

The force of interest is modelled by a homogeneous time‐continuous Markov chain with finite state space. Ordinary differential equations are obtained for expected values of various functionals of this process, in particular for moments of present values of payment streams that may be deterministic or, possibly, also stochastic and driven by a time‐continuous Markov chain. The homogeneity of the interest process gives rise to explicit formulae for expected values of some stationary functionals, e.g. moments of a perpetuity. Applications are made to some standard forms of insurance.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:apsmda:v:11:y:1995:i:3:p:245-256
    DOI: 10.1002/asm.3150110306
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    Cited by:

    1. Guglielmo D’Amico & Fulvio Gismondi & Filippo Petroni, 2020. "Insurance Contracts for Hedging Wind Power Uncertainty," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    2. 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.
    3. Ethem Çanakoğlu & Süleyman Özekici, 2009. "Portfolio selection in stochastic markets with exponential utility functions," Annals of Operations Research, Springer, vol. 166(1), pages 281-297, February.

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