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On the forward rate concept in multi-state life insurance

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  • Marcus Christiansen
  • Andreas Niemeyer

Abstract

Similarly to the notion of modeling credit risk by using forward credit default spread rates, mortality risk in life insurance contracts is nowadays often modeled by using forward mortality (spread) rates. More recently, this concept has also been discussed for more complex life insurances that include multiple lives or intermediate states that correspond to the health status of the insured. For consistency purposes and for technical reasons, most authors assume that the underlying financial and demographic events are stochastically independent. In the present paper, we study sufficient and necessary conditions under which general transition forward rates are indeed consistent with respect to the relevant insurance claims. This shows the theoretical limitations of the forward rate concept in life insurance. Our study is based on a model where the underlying financial and demographical developments are diffusion processes driven by a multivariate Brownian motion. This allows us to investigate independence properties by analyzing the asymptotic behavior of mixed (conditional) moments. In particular, we obtain that for joint life and disability insurance policies, some specific demographic events need to be dependent in order to ensure consistency. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Marcus Christiansen & Andreas Niemeyer, 2015. "On the forward rate concept in multi-state life insurance," Finance and Stochastics, Springer, vol. 19(2), pages 295-327, April.
    • Handle: RePEc:spr:finsto:v:19:y:2015:i:2:p:295-327
    DOI: 10.1007/s00780-014-0244-9
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    References listed on IDEAS

    as
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    Cited by:

    1. Kristian Buchardt & Christian Furrer & Mogens Steffensen, 2019. "Forward transition rates," Finance and Stochastics, Springer, vol. 23(4), pages 975-999, October.
    2. K. Buchardt & C. Furrer & M. Steffensen, 2018. "Forward transition rates," Papers 1811.00137, arXiv.org, revised Apr 2019.
    3. Theis Bathke & Marcus Christiansen, 2022. "Two-dimensional forward and backward transition rates," Papers 2204.12766, arXiv.org.

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    More about this item

    Keywords

    Forward mortality rate; Multi-state life insurance; Multiple default; Moment estimates for diffusion processes; Securitization of demographic risk; 60J60; 91B30; 91G30; 91G40; G12; G22;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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