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Practical and theoretical aspects of market-consistent valuation and hedging of insurance liabilities

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  • Łukasz Delong

    (Warsaw School of Economics)

Abstract

In this paper we deal with market-consistent valuation and hedging of insurance cash flows. We start with recalling traditional actuarial and financial pricing principles and we show how to integrate them into one arbitrage-free principle which leads to market-consistent valuation of the cash flows. Integrated actuarial and financial valuation is justified by referring to Solvency II Directive and discussing its key points related to market-consistent valuation. As an arbitrage-free pricing principle requires specification of an equivalent martingale measure, we characterize all equivalent martingale measures in a very general combined insurance and financial model. This full characterization allows us to price all claims contingent on the financial and insurance risks. We also deal with static and dynamic hedging of insurance liabilities in our general model. We derive an investment portfolio consisting of a bond, a stock and a mortality bond which can be used by a life insurance company to hedge its payment process contingent on the financial and insurance risk. The goal is to unify practical and theoretical aspects of market-consistent valuation and hedging and to state general results relevant to insurance applications.

Suggested Citation

  • 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.
    • Handle: RePEc:nbp:nbpbik:v:42:y:2011:i:1:p:49-78
    Note: This research is supported by the Foundation for Polish Science. The author would like to thank two anonymous referees for their useful remarks that improved the earlier version of this paper.
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    References listed on IDEAS

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    1. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Martellini, Lionel, 2005. "Dynamic asset pricing theory with uncertain time-horizon," Journal of Economic Dynamics and Control, Elsevier, vol. 29(10), pages 1737-1764, October.
    2. Møller,Thomas & Steffensen,Mogens, 2007. "Market-Valuation Methods in Life and Pension Insurance," Cambridge Books, Cambridge University Press, number 9780521868778.
    3. Christophette Blanchet-Scalliet & Monique Jeanblanc, 2004. "Hazard rate for credit risk and hedging defaultable contingent claims," Finance and Stochastics, Springer, vol. 8(1), pages 145-159, January.
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    Cited by:

    1. 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.
    2. Florian Gach & Simon Hochgerner & Eva Kienbacher & Gabriel Schachinger, 2023. "Mean-field Libor market model and valuation of long term guarantees," Papers 2310.09022, arXiv.org, revised Nov 2023.

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    More about this item

    Keywords

    Integrated actuarial and financial valuation; equivalent martingale measure; martingale representation theorem; static and dynamic hedging; mortality bond; Solvency II;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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