IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v3y2015i3p290-317d53175.html
   My bibliography  Save this article

Life Insurance Cash Flows with Policyholder Behavior

Author

Listed:
  • Kristian Buchardt

    (PFA Pension, Sundkrogsgade 4, DK-2100 Copenhagen Ø, Denmark
    Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark)

  • Thomas Møller

    (PFA Pension, Sundkrogsgade 4, DK-2100 Copenhagen Ø, Denmark
    Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark)

Abstract

The problem of the valuation of life insurance payments with policyholder behavior is studied. First, a simple survival model is considered, and it is shown how cash flows without policyholder behavior can be modified to include surrender and free policy behavior by calculation of simple integrals. In the second part, a more general disability model with recovery is studied. Here, cash flows are determined by solving a modified Kolmogorov forward differential equation. We conclude the paper with numerical examples illustrating the methods proposed and the impact of policyholder behavior.

Suggested Citation

  • Kristian Buchardt & Thomas Møller, 2015. "Life Insurance Cash Flows with Policyholder Behavior," Risks, MDPI, vol. 3(3), pages 1-28, July.
    • Handle: RePEc:gam:jrisks:v:3:y:2015:i:3:p:290-317:d:53175
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/3/3/290/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/3/3/290/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Buchardt, Kristian, 2014. "Dependent interest and transition rates in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 167-179.
    2. Møller,Thomas & Steffensen,Mogens, 2007. "Market-Valuation Methods in Life and Pension Insurance," Cambridge Books, Cambridge University Press, number 9780521868778, November.
    3. Steffensen, Mogens, 2002. "Intervention options in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 71-85, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ahmad, Jamaal & Bladt, Mogens & Furrer, Christian, 2023. "Aggregate Markov models in life insurance: Properties and valuation," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 50-69.
    2. Jamaal Ahmad & Mogens Bladt, 2022. "Phase-type representations of stochastic interest rates with applications to life insurance," Papers 2207.11292, arXiv.org, revised Nov 2022.
    3. Christiansen, Marcus C. & Furrer, Christian, 2022. "Extension of as-if-Markov modeling to scaled payments," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 288-306.
    4. Christiansen, Marcus C. & Djehiche, Boualem, 2020. "Nonlinear reserving and multiple contract modifications in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 187-195.
    5. Jamaal Ahmad, 2021. "Multivariate higher order moments in multi-state life insurance," Papers 2102.11714, arXiv.org, revised Oct 2021.
    6. Christian Furrer, 2022. "Scaled insurance cash flows: representation and computation via change of measure techniques," Finance and Stochastics, Springer, vol. 26(2), pages 359-382, April.
    7. Kristian Buchardt & Christian Furrer & Mogens Steffensen, 2019. "Forward transition rates," Finance and Stochastics, Springer, vol. 23(4), pages 975-999, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Buchardt, Kristian, 2014. "Dependent interest and transition rates in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 167-179.
    2. Kristian Buchardt & Christian Furrer & Mogens Steffensen, 2019. "Forward transition rates," Finance and Stochastics, Springer, vol. 23(4), pages 975-999, October.
    3. Debbie Kusch Falden & Anna Kamille Nyegaard, 2021. "Retrospective Reserves and Bonus with Policyholder Behavior," Risks, MDPI, vol. 9(1), pages 1-28, January.
    4. Jamaal Ahmad & Mogens Bladt, 2022. "Phase-type representations of stochastic interest rates with applications to life insurance," Papers 2207.11292, arXiv.org, revised Nov 2022.
    5. Christiansen, Marcus C. & Djehiche, Boualem, 2020. "Nonlinear reserving and multiple contract modifications in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 187-195.
    6. Marco Di Francesco & Roberta Simonella, 2023. "A stochastic Asset Liability Management model for life insurance companies," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 37(1), pages 61-94, March.
    7. Kristian Buchardt & Thomas Møller, 2018. "Hedging and Cash Flows in the Presence of Taxes and Expenses in Life and Pension Insurance," Risks, MDPI, vol. 6(3), pages 1-25, July.
    8. Berdin, Elia & Gründl, Helmut & Kubitza, Christian, 2017. "Rising interest rates, lapse risk, and the stability of life insurers," ICIR Working Paper Series 29/17, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    9. Xavier Milhaud & Christophe Dutang, 2018. "Lapse tables for lapse risk management in insurance: a competing risk approach," Post-Print hal-01985256, HAL.
    10. Kochanski, Michael, 2010. "Solvency capital requirement for German unit-linked insurance products," German Risk and Insurance Review (GRIR), University of Cologne, Department of Risk Management and Insurance, vol. 6(2), pages 33-70.
    11. Ragnar Norberg, 2013. "Optimal hedging of demographic risk in life insurance," Finance and Stochastics, Springer, vol. 17(1), pages 197-222, January.
    12. Magdalena Homa, 2022. "The Impact of MT Strategies on Risk and Value Distribution of Unit-linked Insurance Portfolio," European Research Studies Journal, European Research Studies Journal, vol. 0(3), pages 607-619.
    13. Gerstner, Thomas & Griebel, Michael & Holtz, Markus, 2009. "Efficient deterministic numerical simulation of stochastic asset-liability management models in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 434-446, June.
    14. Youssouf A. F. Toukourou & Franc{c}ois Dufresne, 2015. "ON Integrated Chance Constraints in ALM for Pension Funds," Papers 1503.05343, arXiv.org.
    15. Kei Fukuda & Akihiko Inoue & Yumiharu Nakano, 2007. "Optimal intertemporal risk allocation applied to insurance pricing," Papers 0711.1143, arXiv.org, revised Nov 2007.
    16. Łukasz Delong, 2011. "Practical and theoretical aspects of market-consistent valuation and hedging of insurance liabilities," Bank i Kredyt, Narodowy Bank Polski, vol. 42(1), pages 49-78.
    17. Julian Jetses & Marcus C. Christiansen, 2021. "A General Surplus Decomposition Principle in Life Insurance," Papers 2111.12967, arXiv.org.
    18. Jiwook Jang & Siti Norafidah Mohd Ramli, 2018. "Hierarchical Markov Model in Life Insurance and Social Benefit Schemes," Risks, MDPI, vol. 6(3), pages 1-17, June.
    19. Nielsen, Peter Holm & Steffensen, Mogens, 2008. "Optimal investment and life insurance strategies under minimum and maximum constraints," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 15-28, August.
    20. Jang, Jiwook & Mohd Ramli, Siti Norafidah, 2015. "Jump diffusion transition intensities in life insurance and disability annuity," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 440-451.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jrisks:v:3:y:2015:i:3:p:290-317:d:53175. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.