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Markov chain modeling of policyholder behavior in life insurance and pension

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Abstract

We calculate reserves regarding expected policyholder behavior. The behavior is modeled to occur incidentally similarly to insurance risk. The focus is on multi-state modelling of insurance risk and behavioral risk in terms of free policy risk and surrender risk. We discuss valuation techniques in the cases where behavior is modeled to occur independently or dependently of insurance risk, respectively. Ordinary differential equations make it easier to work with dependence between insurance risk and behavior risk. We analyze the effects of the underlying behavioral assumptions for two contracts. For a “new” contract with low technical interest rate relative to the market interest rate, we obtain the lowest reserve by counting in dependence. For an “old” contract with high technical interest rate relative to the market interest rate, the picture is more blurred, depending on assumptions on reactivation (recovery) and independence.

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Acknowledgments

Work supported by the Danish Advanced Technology Foundation (Højteknologifonden) (017-2010-3).

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark

    Lars Frederik Brandt Henriksen & Mogens Steffensen

  2. Edlund A/S, Bjerregårds Sidevej 4, 2500, Valby, Denmark

    Jeppe Woetmann Nielsen & Christian Svensson

Authors
  1. Lars Frederik Brandt Henriksen
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  2. Jeppe Woetmann Nielsen
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  3. Mogens Steffensen
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  4. Christian Svensson
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Corresponding author

Correspondence to Christian Svensson.

Appendix: A The Danish FSA yield curve used in the market basis

Appendix: A The Danish FSA yield curve used in the market basis

In Fig. 9 we plot the (discretely compounded) yield curve, \(R\), published on 2013-04-08 by the Danish FSA, from which we extracted the equivalent continuous forward rate used in the market basis. We also plot the technical interest rates used in the two contracts considered in Sect. 6.2, here discretely compounded (\(R^* = e^{r^*} - 1\)).

Fig. 9
figure 9

The interest rates used in the bases of the examples

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Henriksen, L.F.B., Nielsen, J.W., Steffensen, M. et al. Markov chain modeling of policyholder behavior in life insurance and pension. Eur. Actuar. J. 4, 1–29 (2014). https://doi.org/10.1007/s13385-014-0091-2

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  • DOI: https://doi.org/10.1007/s13385-014-0091-2

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