IDEAS home Printed from https://ideas.repec.org/p/lar/wpaper/2022-09.html
   My bibliography  Save this paper

Insurance-Finance Arbitrage

Author

Listed:
  • Philippe ARTZNER

    (LaRGE Research Center, Université de Strasbourg)

  • Karl-Theodor EISELE

    (LaRGE Research Center, Université de Strasbourg)

  • Thorsten SCHMIDT

    (Albert-Ludwigs University of Freiburg)

Abstract

Most insurance contracts are inherently linked to financial markets, be it via interest rates, or – as hybrid products like equity-linked life insurance and variable annuities – directly to stocks or indices. However, insurance contracts are not for trade except sometimes as surrender to the selling office. This excludes the situation of arbitrage by buying and selling insurance contracts at different prices. Furthermore, the insurer uses private information on top of the publicly available one about financial market. This paper provides a study of the consistency of insurance contracts in connection with trades in the financial market with explicit mention of the information involved. By defining strategies on an insurance portfolio and combining them with financial trading strategies, we arrive at the notion of insurance-finance arbitrage (IFA). In analogy to the classical fundamental theorem of asset pricing, we give a fundamental theorem on the absence of IFA, leading to the existence of an insurance-finance-consistent probability. In addition, we study when this probability gives the expected discounted cash-flows required by the EIOPA best estimate. The generality of our approach allows to incorporate many important aspects, like mortality risk or general levels of dependence between mortality and stock markets. Utilizing the theory of enlargements of filtrations, we construct a tractable framework for insurance-finance consistent valuation.

Suggested Citation

  • 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.
    • Handle: RePEc:lar:wpaper:2022-09
    as

    Download full text from publisher

    File URL: http://ifs.u-strasbg.fr/large/publications/2022/2022-09.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Irene Klein, 2000. "A Fundamental Theorem of Asset Pricing for Large Financial Markets," Mathematical Finance, Wiley Blackwell, vol. 10(4), pages 443-458, October.
    2. Hainaut, Donatien & Devolder, Pierre & Pelsser, Antoon, 2018. "Robust evaluation of SCR for participating life insurances under Solvency II," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 107-123.
    3. Zhenyu Cui & Runhuan Feng & Anne MacKay, 2017. "Variable Annuities with VIX-Linked Fee Structure under a Heston-Type Stochastic Volatility Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(3), pages 458-483, July.
    4. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    5. 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.
    6. 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).
    7. Lars Niemann & Thorsten Schmidt, 2021. "A conditional version of the second fundamental theorem of asset pricing in discrete time," Papers 2102.13574, arXiv.org, revised May 2023.
    8. Sergio Pulido, 2010. "The fundamental theorem of asset pricing, the hedging problem and maximal claims in financial markets with short sales prohibitions," Papers 1012.3102, arXiv.org, revised Jan 2014.
    9. 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.
    10. Sergio Pulido, 2014. "The fundamental theorem of asset pricing, the hedging problem and maximal claims in financial markets with short sales prohibitions," Post-Print hal-02265271, HAL.
    11. Bühlmann, Hans & Platen, Eckhard, 2003. "A Discrete Time Benchmark Approach for Insurance and Finance," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 153-172, November.
    12. Patrick Cheridito & Michael Kupper, 2011. "Composition Of Time-Consistent Dynamic Monetary Risk Measures In Discrete Time," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 137-162.
    13. Laurence Carassus & Huye^n Pham & Nizar Touzi, 2001. "No Arbitrage in Discrete Time Under Portfolio Constraints," Mathematical Finance, Wiley Blackwell, vol. 11(3), pages 315-329, July.
    14. Schachermayer, W., 1992. "A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 249-257, December.
    15. 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.
    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. Philippe Artzner & Karl-Theodor Eisele & Thorsten Schmidt, 2020. "Insurance-Finance Arbitrage," Papers 2005.11022, arXiv.org, revised Nov 2022.
    2. 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.
    3. 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.
    4. 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.
    5. Karim Barigou & Valeria Bignozzi & Andreas Tsanakas, 2020. "Insurance valuation: A two-step generalised regression approach," Papers 2012.04364, arXiv.org, revised Nov 2021.
    6. Tahir Choulli & Catherine Daveloose & Michèle Vanmaele, 2021. "Mortality/Longevity Risk-Minimization with or without Securitization," Mathematics, MDPI, vol. 9(14), pages 1-27, July.
    7. Claudio Fontana & Wolfgang J. Runggaldier, 2020. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Papers 2006.15563, arXiv.org, revised Sep 2020.
    8. Karim Barigou & Valeria Bignozzi & Andreas Tsanakas, 2021. "Insurance valuation: A two-step generalised regression approach," Working Papers hal-03043244, HAL.
    9. 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.
    10. Fontana, Claudio & Runggaldier, Wolfgang J., 2021. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 66-80.
    11. 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.
    12. 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.
    13. Hampus Engsner & Filip Lindskog & Julie Thoegersen, 2021. "Multiple-prior valuation of cash flows subject to capital requirements," Papers 2109.00306, arXiv.org.
    14. Karim Barigou & Valeria Bignozzi & Andreas Tsanakas, 2021. "Insurance valuation: A two-step generalised regression approach," Post-Print hal-03043244, HAL.
    15. Tak Siu & John Lau & Hailiang Yang, 2007. "On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(3), pages 255-275, September.
    16. T. Marquardt & Eckhard Platen & S. Jaschke, 2008. "Valuing Guaranteed Minimum Death Benefit Options in Variable Annuities Under a Benchmark Approach," Research Paper Series 221, Quantitative Finance Research Centre, University of Technology, Sydney.
    17. Eckhard Platen & Stefan Tappe, 2020. "Exploiting arbitrage requires short selling," Papers 2011.12523, arXiv.org, revised Sep 2022.
    18. Wayne King Ming Chan, 2015. "RAROC-Based Contingent Claim Valuation," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2015.
    19. Jin Sun & Pavel V. Shevchenko & Man Chung Fung, 2018. "The Impact of Management Fees on the Pricing of Variable Annuity Guarantees," Risks, MDPI, vol. 6(3), pages 1-20, September.
    20. Jörn Sass & Manfred Schäl, 2014. "Numeraire portfolios and utility-based price systems under proportional transaction costs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 195-234, October.

    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:lar:wpaper:2022-09. 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: Christophe J. Godlewski (email available below). General contact details of provider: https://edirc.repec.org/data/lastrfr.html .

    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.