IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2109.13796.html
   My bibliography  Save this paper

Actuarial-consistency and two-step actuarial valuations: a new paradigm to insurance valuation

Author

Listed:
  • Karim Barigou

    (ISFA)

  • Daniel Linders

    (UvA)

  • Fan Yang

Abstract

This paper introduces new valuation schemes called actuarial-consistent valuations for insurance liabilities which depend on both financial and actuarial risks, which imposes that all actuarial risks are priced via standard actuarial principles. We propose to extend standard actuarial principles by a new actuarial-consistent procedure, which we call "two-step actuarial valuations". \bluebis{In the case valuations are coherent}, we show that actuarial-consistent valuations are equivalent to two-step actuarial valuations. We also discuss the connection with "two-step market-consistent valuations" from Pelsser and Stadje (2014). In particular, we discuss how the dependence structure between actuarial and financial risks impacts both actuarial-consistent and market-consistent valuations.

Suggested Citation

  • Karim Barigou & Daniel Linders & Fan Yang, 2021. "Actuarial-consistency and two-step actuarial valuations: a new paradigm to insurance valuation," Papers 2109.13796, arXiv.org, revised Mar 2022.
    • Handle: RePEc:arx:papers:2109.13796
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2109.13796
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Antoon Pelsser & Mitja Stadje, 2014. "Time-Consistent And Market-Consistent Evaluations," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 25-65, January.
    2. Nicole El Karoui & Stéphane Loisel & Jean-Luc Prigent & Julien Vedani, 2017. "Market inconsistencies of the market-consistent European life insurance economic valuations: pitfalls and practical solutions," Post-Print hal-01242023, HAL.
    3. Delong, Å ukasz & Dhaene, Jan & Barigou, Karim, 2019. "Fair Valuation Of Insurance Liability Cash-Flow Streams In Continuous Time: Applications," ASTIN Bulletin, Cambridge University Press, vol. 49(2), pages 299-333, May.
    4. Rob Kaas & Marc Goovaerts & Jan Dhaene & Michel Denuit, 2008. "Modern Actuarial Risk Theory," Springer Books, Springer, edition 2, number 978-3-540-70998-5, December.
    5. Ignatieva, Katja & Song, Andrew & Ziveyi, Jonathan, 2016. "Pricing and hedging of guaranteed minimum benefits under regime-switching and stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 286-300.
    6. LUCIANO, Elisa & VIGNA, Elena, 2008. "Mortality risk via affine stochastic intensities: calibration and empirical relevance," MPRA Paper 59627, University Library of Munich, Germany.
    7. Deelstra, Griselda & Devolder, Pierre & Gnameho, Kossi & Hieber, Peter, 2020. "Valuation of hybrid financial and actuarial products in life insurance by a novel three-step method," LIDAM Reprints ISBA 2020020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. 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.
    9. Elisa Luciano & Luca Regis & Elena Vigna, 2017. "Single- and Cross-Generation Natural Hedging of Longevity and Financial Risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 961-986, September.
    10. Dhaene, Jan & Stassen, Ben & Barigou, Karim & Linders, Daniël & Chen, Ze, 2017. "Fair valuation of insurance liabilities: Merging actuarial judgement and market-consistency," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 14-27.
    11. Barigou, Karim & Chen, Ze & Dhaene, Jan, 2019. "Fair dynamic valuation of insurance liabilities: Merging actuarial judgement with market- and time-consistency," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 19-29.
    12. Madan,Dilip & Schoutens,Wim, 2016. "Applied Conic Finance," Cambridge Books, Cambridge University Press, number 9781107151697.
    13. Deelstra, Griselda & Grasselli, Martino & Van Weverberg, Christopher, 2016. "The role of the dependence between mortality and interest rates when pricing Guaranteed Annuity Options," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 205-219.
    14. Fung, Man Chung & Ignatieva, Katja & Sherris, Michael, 2014. "Systematic mortality risk: An analysis of guaranteed lifetime withdrawal benefits in variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 103-115.
    15. Dilip B. Madan & Alexander Cherny, 2010. "Markets As A Counterparty: An Introduction To Conic Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(08), pages 1149-1177.
    16. Deelstra, Griselda & Devolder, Pierre & Gnameho, Kossi & Hieber, Peter, 2020. "Valuation Of Hybrid Financial And Actuarial Products In Life Insurance By A Novel Three-Step Method," ASTIN Bulletin, Cambridge University Press, vol. 50(3), pages 709-742, 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. Karim Barigou & Daniël Linders & Fan yang, 2022. "Actuarial-consistency and two-step actuarial valuations: a new paradigm to insurance valuation," Working Papers hal-03327710, HAL.
    2. Karim Barigou & Daniël Linders & Fan Yang, 2022. "Actuarial-consistency and two-step actuarial valuations: a new paradigm to insurance valuation," Post-Print hal-03327710, HAL.
    3. Karim Barigou & Valeria Bignozzi & Andreas Tsanakas, 2020. "Insurance valuation: A two-step generalised regression approach," Papers 2012.04364, arXiv.org, revised Nov 2021.
    4. Karim Barigou & Lukasz Delong, 2021. "Pricing equity-linked life insurance contracts with multiple risk factors by neural networks," Working Papers hal-02896141, HAL.
    5. Karim Barigou & Valeria Bignozzi & Andreas Tsanakas, 2021. "Insurance valuation: A two-step generalised regression approach," Working Papers hal-03043244, HAL.
    6. Karim Barigou & Valeria Bignozzi & Andreas Tsanakas, 2021. "Insurance valuation: A two-step generalised regression approach," Post-Print hal-03043244, HAL.
    7. Hansjörg Albrecher & Karl‐Theodor Eisele & Mogens Steffensen & Mario V. Wüthrich, 2022. "On the cost‐of‐capital rate under incomplete market valuation," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(4), pages 1139-1158, December.
    8. Karim Barigou & Lukasz Delong, 2020. "Pricing equity-linked life insurance contracts with multiple risk factors by neural networks," Papers 2007.08804, arXiv.org, revised Nov 2021.
    9. Karim Barigou & Lukasz Delong, 2021. "Pricing equity-linked life insurance contracts with multiple risk factors by neural networks," Post-Print hal-02896141, HAL.
    10. Chen, Ze & Chen, Bingzheng & Dhaene, Jan & Yang, Tianyu, 2021. "Fair dynamic valuation of insurance liabilities via convex hedging," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 1-13.
    11. Tahir Choulli & Catherine Daveloose & Michèle Vanmaele, 2021. "Mortality/Longevity Risk-Minimization with or without Securitization," Mathematics, MDPI, vol. 9(14), pages 1-27, July.
    12. Delong, Łukasz & Dhaene, Jan & Barigou, Karim, 2019. "Fair valuation of insurance liability cash-flow streams in continuous time: Theory," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 196-208.
    13. Engsner, Hampus & Lindskog, Filip & Thøgersen, Julie, 2023. "Multiple-prior valuation of cash flows subject to capital requirements," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 41-56.
    14. Philippe ARTZNER & Karl-Theodor EISELE & Thorsten SCHMIDT, 2022. "Insurance-Finance Arbitrage," Working Papers of LaRGE Research Center 2022-09, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg.
    15. Hampus Engsner & Filip Lindskog & Julie Thoegersen, 2021. "Multiple-prior valuation of cash flows subject to capital requirements," Papers 2109.00306, arXiv.org.
    16. Koch-Medina, Pablo & Moreno-Bromberg, Santiago & Ravanelli, Claudia & Šikić, Mario, 2021. "Revisiting optimal investment strategies of value-maximizing insurance firms," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 131-151.
    17. Huang, Yiming & Mamon, Rogemar & Xiong, Heng, 2022. "Valuing guaranteed minimum accumulation benefits by a change of numéraire approach," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 1-26.
    18. Barigou, Karim & Chen, Ze & Dhaene, Jan, 2019. "Fair dynamic valuation of insurance liabilities: Merging actuarial judgement with market- and time-consistency," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 19-29.
    19. Wenlong Hu, 2020. "Risk management of guaranteed minimum maturity benefits under stochastic mortality and regime-switching by Fourier space time-stepping framework," Papers 2006.15483, arXiv.org, revised Dec 2020.
    20. Francesco Della Corte & Gian Paolo Clemente & Nino Savelli, 2023. "A cohort-based Partial Internal Model for demographic risk," Papers 2307.03090, arXiv.org.

    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:2109.13796. 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.