IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2102.10047.html
   My bibliography  Save this paper

Thiele's Differential Equation Based on Markov Jump Processes with Non-countable State Space

Author

Listed:
  • Emmanuel Coffie
  • Sindre Duedahl
  • Frank Proske

Abstract

In modern life insurance, Markov processes in continuous time on a finite or at least countable state space have been over the years an important tool for the modelling of the states of an insured. Motivated by applications in disability insurance, we propose in this paper a model for insurance states based on Markov jump processes with more general state spaces. We use this model to derive a new type of Thiele's differential equation which e.g. allows for a consistent calculation of reserves in disability insurance based on two-parameter continuous time rehabilitation rates.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2102.10047
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2102.10047
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Møller,Thomas & Steffensen,Mogens, 2007. "Market-Valuation Methods in Life and Pension Insurance," Cambridge Books, Cambridge University Press, number 9780521868778, January.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    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. Gerstner, Thomas & Griebel, Michael & Holtz, Markus & Goschnick, Ralf & Haep, Marcus, 2008. "A general asset-liability management model for the efficient simulation of portfolios of life insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 704-716, April.
    2. Jonas Alm & Filip Lindskog, 2015. "Valuation of Index-Linked Cash Flows in a Heath–Jarrow–Morton Framework," Risks, MDPI, vol. 3(3), pages 1-27, September.
    3. Ec. Ana Preda, Ph. D Student, Lect. Mirela Monea Ph. D, 2011. "Theunit-Linkedinsurance- A Formof Long Termeconomizing In Thecontext Of Globalcrisis," Annals of University of Craiova - Economic Sciences Series, University of Craiova, Faculty of Economics and Business Administration, vol. 4(39), pages 251-258, May.
    4. Noël Bonneuil, 2013. "Early Warning to Insolvency in the Pension Fund: The French Case," Risks, MDPI, vol. 1(1), pages 1-13, January.
    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. Guglielmo D’Amico & Fulvio Gismondi & Filippo Petroni, 2020. "Insurance Contracts for Hedging Wind Power Uncertainty," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    9. Jamaal Ahmad & Kristian Buchardt & Christian Furrer, 2020. "Computation of bonus in multi-state life insurance," Papers 2007.04051, arXiv.org, revised Nov 2023.
    10. Djehiche, Boualem & Löfdahl, Björn, 2016. "Nonlinear reserving in life insurance: Aggregation and mean-field approximation," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 1-13.
    11. Ana Preda & Mirela Monea, 2011. "Impact of the Financial Crisis on Life Insurance in Romania," Annals of the University of Petrosani, Economics, University of Petrosani, Romania, vol. 11(4), pages 245-254.
    12. Ragnar Norberg, 2013. "Optimal hedging of demographic risk in life insurance," Finance and Stochastics, Springer, vol. 17(1), pages 197-222, January.
    13. 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.
    14. Oytun Hac{c}ar{i}z & Torsten Kleinow & Angus S. Macdonald, 2023. "On Technical Bases and Surplus in Life Insurance," Papers 2310.16927, arXiv.org.
    15. Marius D. Pascariu & Ugofilippo Basellini & José Manuel Aburto & Vladimir Canudas-Romo, 2020. "The Linear Link: Deriving Age-Specific Death Rates from Life Expectancy," Risks, MDPI, vol. 8(4), pages 1-18, October.
    16. 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.
    17. Youssouf A. F. Toukourou & Franc{c}ois Dufresne, 2015. "ON Integrated Chance Constraints in ALM for Pension Funds," Papers 1503.05343, arXiv.org.
    18. Bojan Baškot, 2013. "Modelling Home Equity Conversion Loans With Life Insurance Models," Economic Annals, Faculty of Economics and Business, University of Belgrade, vol. 58(199), pages 127-164, October -.
    19. Kei Fukuda & Akihiko Inoue & Yumiharu Nakano, 2007. "Optimal intertemporal risk allocation applied to insurance pricing," Papers 0711.1143, arXiv.org, revised Nov 2007.
    20. Kristian Buchardt & Christian Furrer & Mogens Steffensen, 2019. "Forward transition rates," Finance and Stochastics, Springer, vol. 23(4), pages 975-999, October.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:2102.10047. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.