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Fair valuation of insurance liabilities via mean-variance hedging in a multi-period setting

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  • Karim Barigou
  • Jan Dhaene

Abstract

A general class of fair valuations which are both market-consistent (mark-to-market for any hedgeable part of a claim) and actuarial (mark-to-model for any claim that is independent of financial market evolutions) was introduced in Dhaene et al. [Insurance: Mathematics & Economics, 76, 14–27 (2017)] in a single period framework. In particular, the authors considered mean-variance hedge-based (MVHB) valuations where fair valuations of insurance liabilities are expressed in terms of mean-variance hedges and actuarial valuations. In this paper, we generalize this MVHB approach to a multi-period dynamic investment setting. We show that the classes of fair valuations and MVHB valuations are equivalent in this generalized setting. We derive tractable formulas for the fair valuation of equity-linked contracts and show how the actuarial part of their MVHB valuation decomposes into a diversifiable and a non-diversifiable component.

Suggested Citation

  • Karim Barigou & Jan Dhaene, 2019. "Fair valuation of insurance liabilities via mean-variance hedging in a multi-period setting," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2019(2), pages 163-187, February.
    • Handle: RePEc:taf:sactxx:v:2019:y:2019:i:2:p:163-187
    DOI: 10.1080/03461238.2018.1528477
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    Cited by:

    1. Chen, Ze & Feng, Runhuan & Li, Hong & Yang, Tianyu, 2024. "Coping with longevity via hedging: Fair dynamic valuation of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 154-169.
    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. Chen, Damiaan H.J. & Beetsma, Roel M.W.J. & van Wijnbergen, Sweder J.G., 2023. "Intergenerational sharing of unhedgeable inflation risk," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 140-160.
    4. Motte, Edouard & Hainaut, Donatien, 2024. "Efficient hedging of life insurance portfolio for loss-averse insurers," LIDAM Discussion Papers ISBA 2024013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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