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On the cost‐of‐capital rate under incomplete market valuation

Author

Listed:
  • Hansjörg Albrecher
  • Karl‐Theodor Eisele
  • Mogens Steffensen
  • Mario V. Wüthrich

Abstract

In this paper we discuss the concept of the cost‐of‐capital (CoC) rate for an insurance company as an equilibrium in the economic triangle of policyholders, shareholders, and the regulator. This provides a possible rationalization and an economic foundation for a quantity that is widely used in practice but whose value is typically neither technically nor economically well justified. We show how it can be well founded in such a triangular equilibrium. Under a simple one‐period model and a valuation procedure of a two‐price economy for illiquid assets we provide a corresponding economic‐theoretical quantification for the CoC rate. The resulting rates are illustrated by a number of concrete numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jrinsu:v:89:y:2022:i:4:p:1139-1158
    DOI: 10.1111/jori.12406
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    References listed on IDEAS

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    1. Denuit, Michel, 2019. "Size-Biased Transform And Conditional Mean Risk Sharing, With Application To P2p Insurance And Tontines," ASTIN Bulletin, Cambridge University Press, vol. 49(3), pages 591-617, September.
    2. Zeddouk, Fadoua & Devolder, Pierre, 2019. "Pricing of Longevity Derivatives and Cost of Capital," LIDAM Reprints ISBA 2019033, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Delong, Łukasz & 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. 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).
    5. Chia‐Chun Chiang & Hugh Hoikwang Kim & Greg Niehaus, 2022. "Opaque liabilities, learning, and the cost of equity capital for insurers," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(4), pages 1031-1076, December.
    6. Hampus Engsner & Filip Lindskog & Julie Thoegersen, 2021. "Multiple-prior valuation of cash flows subject to capital requirements," Papers 2109.00306, arXiv.org.
    7. Denuit, Michel, 2020. "Investing in your own and peers’ risks: the simple analytics of P2P insurance," LIDAM Reprints ISBA 2020026, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Ernst Eberlein & Dilip Madan & Martijn Pistorius & Wim Schoutens & Marc Yor, 2014. "Two price economies in continuous time," Annals of Finance, Springer, vol. 10(1), pages 71-100, February.
    9. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    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. Fadoua Zeddouk & Pierre Devolder, 2019. "Pricing of Longevity Derivatives and Cost of Capital," Risks, MDPI, vol. 7(2), pages 1-29, April.
    12. 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.
    13. Malamud, Semyon & Trubowitz, Eugene & Wüthrich, Mario V., 2008. "Market Consistent Pricing of Insurance Products," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 483-526, November.
    14. 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.
    15. Denuit, Michel, 2019. "Size-biased transform and conditional mean risk sharing, with application to P2P insurance and tontines," LIDAM Discussion Papers ISBA 2019010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    16. Hampus Engsner & Kristoffer Lindensjö & Filip Lindskog, 2020. "The value of a liability cash flow in discrete time subject to capital requirements," Finance and Stochastics, Springer, vol. 24(1), pages 125-167, January.
    17. Markus Huggenberger & Peter Albrecht, 2022. "Risk pooling and solvency regulation: A policyholder's perspective," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(4), pages 907-950, December.
    18. Denuit, Michel, 2019. "Size-biased transform and conditional mean risk sharing, with application to P2P insurance and tontines," LIDAM Reprints ISBA 2019038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Damir Filipović & Robert Kremslehner & Alexander Muermann, 2015. "Optimal Investment and Premium Policies Under Risk Shifting and Solvency Regulation," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 82(2), pages 261-288, June.
    20. 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.
    21. 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.
    22. Bauer, Daniel & Zanjani, George, 2021. "Economic capital and RAROC in a dynamic model," Journal of Banking & Finance, Elsevier, vol. 125(C).
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    Cited by:

    1. Christoph Moehr, 2023. "A framework for the valuation of insurance liabilities by production cost," Papers 2401.00263, arXiv.org.

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