IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2409.00780.html
   My bibliography  Save this paper

A functional variational approach to pricing path dependent insurance policies

Author

Listed:
  • David R. Ba~nos
  • Salvador Ortiz-Latorre
  • Oriol Zamora Font

Abstract

The main purpose of this work is the derivation of a functional partial differential equation (FPDE) for the calculations of equity-linked insurance policies, where the payment stream may depend on the whole past history of the financial asset. To this end, we employ variational techniques from the theory of functional It\^o calculus.

Suggested Citation

  • David R. Ba~nos & Salvador Ortiz-Latorre & Oriol Zamora Font, 2024. "A functional variational approach to pricing path dependent insurance policies," Papers 2409.00780, arXiv.org.
    • Handle: RePEc:arx:papers:2409.00780
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2409.00780
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Aase Nielsen, J. & Sandmann, Klaus, 1995. "Equity-linked life insurance: A model with stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 16(3), pages 225-253, July.
    2. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, vol. 3(3), pages 195-213, June.
    3. Svein-Arne Persson, 1998. "Stochastic interest rate in life insurance: The principle of equivalence revisited," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 1998(2), pages 97-112.
    4. David Baños & Marc Lagunas-Merino & Salvador Ortiz-Latorre, 2020. "Variance and Interest Rate Risk in Unit-Linked Insurance Policies," Risks, MDPI, vol. 8(3), pages 1-23, August.
    5. David R. Ba~nos & Marc Lagunas-Merino & Salvador Ortiz-Latorre, 2020. "Variance and interest rate risk in unit-linked insurance policies," Papers 2006.14833, arXiv.org.
    6. Ragnar Norberg & Christian Max Møller, 1996. "Thiele's differential equation with stochastic interest of diffusion type," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 1996(1), pages 37-49.
    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. David R. Ba~nos, 2020. "Life insurance policies with cash flows subject to random interest rate changes," Papers 2012.15541, arXiv.org.
    2. Bernard, Carole & Boyle, Phelim P., 2011. "A Natural Hedge for Equity Indexed Annuities," Annals of Actuarial Science, Cambridge University Press, vol. 5(2), pages 211-230, September.
    3. Grosen, Anders & Lochte Jorgensen, Peter, 2000. "Fair valuation of life insurance liabilities: The impact of interest rate guarantees, surrender options, and bonus policies," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 37-57, February.
    4. Melnikov, Alexander & Tong, Shuo, 2014. "Valuation of finance/insurance contracts: Efficient hedging and stochastic interest rates modeling," Risk and Decision Analysis, IOS Press, issue 5, pages 23-41.
    5. Hürlimann, Werner, 2010. "Analytical Pricing of the Unit-Linked Endowment with Guarantees and Periodic Premiums," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 631-653, November.
    6. Gao, Quansheng & He, Ting & Zhang, Chi, 2011. "Quantile hedging for equity-linked life insurance contracts in a stochastic interest rate economy," Economic Modelling, Elsevier, vol. 28(1-2), pages 147-156, January.
    7. Kevin Fergusson & Eckhard Platen, 2013. "Real World Pricing of Long Term Cash-Linked Annuities and Equity-Linked Annuities with Cash-Linked Guarantees," Research Paper Series 338, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Steinar Ekern & Svein-Arne Persson, 1996. "Exotic Unit-Linked Life Insurance Contracts," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 21(1), pages 35-63, June.
    9. Nielsen, J. Aase & Sandmann, Klaus & Schlögl, Erik, 2011. "Equity-linked pension schemes with guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 547-564.
    10. Leunglung Chan & Eckhard Platen, 2016. "Pricing of long dated equity-linked life insurance contracts," Published Paper Series 2016-5, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    11. Olivier Le Courtois & François Quittard-Pinon, 2008. "Fair Valuation of Participating Life Insurance Contracts with Jump Risk," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 33(2), pages 106-136, December.
    12. Barbarin, Jerome & Devolder, Pierre, 2005. "Risk measure and fair valuation of an investment guarantee in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 297-323, October.
    13. Jacques, Michel, 2003. "A risk management approach to the pricing of a single equity-linked contract," Journal of Pension Economics and Finance, Cambridge University Press, vol. 2(2), pages 159-179, July.
    14. Gao, Quansheng & He, Ting & Zhang, Chi, 2011. "Quantile hedging for equity-linked life insurance contracts in a stochastic interest rate economy," Economic Modelling, Elsevier, vol. 28(1), pages 147-156.
    15. Coleman, Thomas F. & Li, Yuying & Patron, Maria-Cristina, 2006. "Hedging guarantees in variable annuities under both equity and interest rate risks," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 215-228, April.
    16. Thomas Poufinas, 2015. "On the pricing of regular premium variable annuities using options," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 4(1), pages 54-77.
    17. Guillen, Montserrat & Jorgensen, Peter Lochte & Nielsen, Jens Perch, 2006. "Return smoothing mechanisms in life and pension insurance: Path-dependent contingent claims," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 229-252, April.
    18. Belssing Taruvinga, 2019. "Solving Selected Problems on American Option Pricing with the Method of Lines," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2019, January-A.
    19. Masahiko Egami & Hideki Iwaki, 2007. "An optimal life insurance policy in the investment-consumption problem in an incomplete market," Papers 0801.0195, arXiv.org, revised May 2011.
    20. Jensen, Bjarne Astrup & Sørensen, Carsten, 2000. "Paying for minimum interest rate guarantees: Who should compensate who?," Working Papers 2000-1, Copenhagen Business School, Department of Finance.

    More about this item

    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:2409.00780. 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.