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Hattendorff Differential Equation for Multi-State Markov Insurance Models

Author

Listed:
  • Rajeev Rajaram

    (Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA
    These authors contributed equally to this work.)

  • Nathan Ritchey

    (Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA
    These authors contributed equally to this work.)

Abstract

We derive a Hattendorff differential equation and a recursion governing the evolution of continuous and discrete time evolution respectively of the variance of the loss at time t random variable given that the state at time t is j , for a multistate Markov insurance model (denoted by 2 σ t ( j ) ). We also show using matrix notation that both models can be easily adapted for use in MATLAB for numerical computations.

Suggested Citation

  • Rajeev Rajaram & Nathan Ritchey, 2021. "Hattendorff Differential Equation for Multi-State Markov Insurance Models," Risks, MDPI, vol. 9(9), pages 1-19, September.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:9:p:169-:d:637086
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    References listed on IDEAS

    as
    1. Dickson,David C. M. & Hardy,Mary R. & Waters,Howard R., 2020. "Solutions Manual for Actuarial Mathematics for Life Contingent Risks," Cambridge Books, Cambridge University Press, number 9781108747615.
    2. Norberg, Ragnar, 1995. "Differential equations for moments of present values in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 17(2), pages 171-180, October.
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    Cited by:

    1. Rajeev Rajaram & Nathan Ritchey, 2023. "Simultaneous Exact Controllability of Mean and Variance of an Insurance Policy," Mathematics, MDPI, vol. 11(15), pages 1-16, July.

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