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Fair valuation of insurance liabilities: Merging actuarial judgement and market-consistency

Author

Listed:
  • Jan Dhaene
  • Ben Stassen
  • Karim Barigou
  • Daniël Linders
  • Ze Chen

Abstract

In this paper, we investigate a single period framework for the fair valuation of the liabilities related to an insurance policy or portfolio.We de ne a fair valuation as a valuation which is both market-consistent (mark-to-market for hedgeable claims)and actuarial (mark-to-model for unhedgeable claims). We introduce the class of hedge-based valuations, where in a rst step of the valuation process, a best hedge for the liability is set up, based on the traded assets in the market, while in a second step, the remaining part of the claim is valuated via an actuarial valuation. We also introduce the class of two-step valuations, the elements of which are closely related to the two-step valuations which were introduced in Pelsser and Stadje (2014). We show that the 3 classes of fair, hedge-based and two-step valuations are identical.

Suggested Citation

  • Jan Dhaene & Ben Stassen & Karim Barigou & Daniël Linders & Ze Chen, 2017. "Fair valuation of insurance liabilities: Merging actuarial judgement and market-consistency," Working Papers Department of Accountancy, Finance and Insurance (AFI), Leuven 578281, KU Leuven, Faculty of Economics and Business (FEB), Department of Accountancy, Finance and Insurance (AFI), Leuven.
    • Handle: RePEc:ete:afiper:578281
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    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. Stadje, M.A. & Pelsser, A., 2014. "Time-Consistent and Market-Consistent Evaluations (Revised version of 2012-086)," Discussion Paper 2014-002, Tilburg University, Center for Economic Research.
    3. Brennan, Michael J & Schwartz, Eduardo S, 1979. "Alternative Investment Strategies for the Issuers of Equity Linked Life Insurance Policies with an Asset Value Guarantee," The Journal of Business, University of Chicago Press, vol. 52(1), pages 63-93, January.
    4. Pelsser, Antoon & Salahnejhad Ghalehjooghi, Ahmad, 2016. "Time-consistent actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 97-112.
    5. Dhaene, Jan & Stassen, Ben & Devolder, Pierre & Vellekoop, Michel, 2014. "The Minimal Entropy Martingale Measure in a market of traded financial and actuarial risks," LIDAM Discussion Papers ISBA 2014055, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. 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.
    7. Tsanakas, Andreas & Wüthrich, Mario V. & Černý, Aleš, 2013. "Market Value Margin Via Mean–Variance Hedging," ASTIN Bulletin, Cambridge University Press, vol. 43(3), pages 301-322, September.
    8. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, April.
    9. Marek Musiela & Thaleia Zariphopoulou, 2004. "A valuation algorithm for indifference prices in incomplete markets," Finance and Stochastics, Springer, vol. 8(3), pages 399-414, August.
    10. 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.
    11. Barrieu, Pauline & El Karoui, Nicole, 2005. "Inf-convolution of risk measures and optimal risk transfer," LSE Research Online Documents on Economics 2829, London School of Economics and Political Science, LSE Library.
    12. Marco Frittelli, 2000. "The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 39-52, January.
    13. Łukasz Delong, 2011. "Practical and theoretical aspects of market-consistent valuation and hedging of insurance liabilities," Bank i Kredyt, Narodowy Bank Polski, vol. 42(1), pages 49-78.
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    Keywords

    Fair valuation of insurance liabilities; market-consistent valuation; actuarial valuation; Solvency II; mean-variance hedging;
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