IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v26y2022i2d10.1007_s00780-022-00472-z.html
   My bibliography  Save this article

Scaled insurance cash flows: representation and computation via change of measure techniques

Author

Listed:
  • Christian Furrer

    (University of Copenhagen)

Abstract

We consider general multi-state life insurance payment processes and study the expected accumulated cash flows that arise when modifying the payments by scaling factors depending on the time of occurrence of specific events. Such modified payment processes arise naturally in the context of incidental policyholder behaviour. We associate to the modifications new probability measures which allow a standard representation of the expected accumulated cash flows. The measures are characterised in terms of the original measure and the scaling factors. Examples for Markov chains illuminate the relevance of our concepts and results to actuarial practice.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:finsto:v:26:y:2022:i:2:d:10.1007_s00780-022-00472-z
    DOI: 10.1007/s00780-022-00472-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00780-022-00472-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00780-022-00472-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kardaras, Constantinos & Kreher, Dörte & Nikeghbali, Ashkan, 2015. "Strict local martingales and bubbles," LSE Research Online Documents on Economics 64967, London School of Economics and Political Science, LSE Library.
    2. Peter Carr & Travis Fisher & Johannes Ruf, 2014. "On the hedging of options on exploding exchange rates," Finance and Stochastics, Springer, vol. 18(1), pages 115-144, January.
    3. 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.
    4. Kristian Buchardt & Christian Furrer & Mogens Steffensen, 2019. "Forward transition rates," Finance and Stochastics, Springer, vol. 23(4), pages 975-999, October.
    5. Milbrodt, Hartmut & Stracke, Andrea, 1997. "Markov models and Thiele's integral equations for the prospective reserve," Insurance: Mathematics and Economics, Elsevier, vol. 19(3), pages 187-235, May.
    6. Kristian Buchardt & Thomas Møller, 2015. "Life Insurance Cash Flows with Policyholder Behavior," Risks, MDPI, vol. 3(3), pages 1-28, July.
    7. K. Buchardt & C. Furrer & M. Steffensen, 2018. "Forward transition rates," Papers 1811.00137, arXiv.org, revised Apr 2019.
    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. 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.

    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. 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. 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.
    3. Thomas Krabichler & Josef Teichmann, 2020. "A constraint-based notion of illiquidity," Papers 2004.12394, arXiv.org.
    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. Johannes Muhle-Karbe & Marcel Nutz, 2018. "A risk-neutral equilibrium leading to uncertain volatility pricing," Finance and Stochastics, Springer, vol. 22(2), pages 281-295, April.
    6. Petteri Piiroinen & Lassi Roininen & Martin Simon, 2019. "Brexit Risk Implied by the SABR Martingale Defect in the EUR-GBP Smile," Papers 1912.05773, arXiv.org, revised Mar 2020.
    7. Antoine Jacquier & Martin Keller-Ressel, 2015. "Implied volatility in strict local martingale models," Papers 1508.04351, arXiv.org.
    8. Peter Imkeller & Nicolas Perkowski, 2015. "The existence of dominating local martingale measures," Finance and Stochastics, Springer, vol. 19(4), pages 685-717, October.
    9. Theis Bathke & Marcus Christiansen, 2022. "Two-dimensional forward and backward transition rates," Papers 2204.12766, arXiv.org.
    10. Kreher, Dörte & Nikeghbali, Ashkan, 2015. "A new kind of augmentation of filtrations suitable for a change of probability measure by a strict local martingale," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 94-101.
    11. Christiansen, Marcus C. & Furrer, Christian, 2021. "Dynamics of state-wise prospective reserves in the presence of non-monotone information," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 81-98.
    12. Marcus C. Christiansen & Christian Furrer, 2020. "Dynamics of state-wise prospective reserves in the presence of non-monotone information," Papers 2003.02173, arXiv.org, revised Jan 2021.
    13. Li, Xue-Mei, 2017. "Strict local martingales: Examples," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 65-68.
    14. Debbie Kusch Falden & Anna Kamille Nyegaard, 2021. "Retrospective Reserves and Bonus with Policyholder Behavior," Risks, MDPI, vol. 9(1), pages 1-28, January.
    15. 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.
    16. Marcus C. Christiansen & Michel M. Denuit & Jan Dhaene, 2014. "Reserve-Dependent Benefits and Costs in Life and Health Insurance Contracts," Tinbergen Institute Discussion Papers 14-117/IV/DSF80, Tinbergen Institute.
    17. Kruse, T. & Popier, A., 2016. "Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2554-2592.
    18. Johannes Ruf & Wolfgang Runggaldier, 2013. "A Systematic Approach to Constructing Market Models With Arbitrage," Papers 1309.1988, arXiv.org, revised Dec 2013.
    19. Erhan Bayraktar & Xiang Yu, 2018. "On the market viability under proportional transaction costs," Mathematical Finance, Wiley Blackwell, vol. 28(3), pages 800-838, July.
    20. Irina Penner & Anthony Reveillac, 2013. "Risk measures for processes and BSDEs," Papers 1304.4853, arXiv.org.

    More about this item

    Keywords

    Multi-state life insurance; Incidental policyholder behaviour; Jump processes; Föllmer measures;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

    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:spr:finsto:v:26:y:2022:i:2:d:10.1007_s00780-022-00472-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.