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Optimal hedging of demographic risk in life insurance

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  • Ragnar Norberg

Abstract

A Markov chain model is taken to describe the development of a multi-state life insurance policy or portfolio in a stochastic economic–demographic environment. It is assumed that there exists an arbitrage-free market with tradeable securities derived from demographic indices. Adopting a mean-variance criterion, two problems are formulated and solved. First, how can an insurer optimally hedge environmental risk by trading in a given set of derivatives? Second, assuming that insurers perform optimal hedging strategies in a given derivatives market, how can the very derivatives be designed in order to minimize the average hedging error across a given population of insurers? The paper comes with the caveat emptor that the theory will find its prime applications, not in securitization of longevity risk, but rather in securitization of catastrophic mortality risk. Copyright Springer-Verlag 2013

Suggested Citation

  • Ragnar Norberg, 2013. "Optimal hedging of demographic risk in life insurance," Finance and Stochastics, Springer, vol. 17(1), pages 197-222, January.
    • Handle: RePEc:spr:finsto:v:17:y:2013:i:1:p:197-222
    DOI: 10.1007/s00780-012-0182-3
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    References listed on IDEAS

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    1. Norberg, Ragnar, 2003. "The Markov Chain Market," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 265-287, November.
    2. Ragnar Norberg, 1999. "A theory of bonus in life insurance," Finance and Stochastics, Springer, vol. 3(4), pages 373-390.
    3. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
    4. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 79-120, May.
    5. Dahl, Mikkel & Moller, Thomas, 2006. "Valuation and hedging of life insurance liabilities with systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 193-217, October.
    6. Møller,Thomas & Steffensen,Mogens, 2007. "Market-Valuation Methods in Life and Pension Insurance," Cambridge Books, Cambridge University Press, number 9780521868778, October.
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    Cited by:

    1. P. Kowalczyk-Rólczyńska & П. Ковальчик-Рульчинская, 2016. "Управление демографическим риском в пенсионных системах // Managing the Demographic Risk of Pension Systems," Review of Business and Economics Studies // Review of Business and Economics Studies, Финансовый Университет // Financial University, vol. 4(4), pages 23-31.
    2. Jaap Spreeuw & Iqbal Owadally & Muhammad Kashif, 2022. "Projecting Mortality Rates Using a Markov Chain," Mathematics, MDPI, vol. 10(7), pages 1-18, April.
    3. Meyricke, Ramona & Sherris, Michael, 2014. "Longevity risk, cost of capital and hedging for life insurers under Solvency II," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 147-155.
    4. Francesca Biagini & Andreas Groll & Jan Widenmann, 2016. "Risk Minimization for Insurance Products via F-Doubly Stochastic Markov Chains," Risks, MDPI, vol. 4(3), pages 1-26, July.

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    More about this item

    Keywords

    Stochastic mortality; Mortality derivatives; Mean-variance hedging; Optimal design of derivatives; 60G55; 62P05; 91B30; 91G20; C02; G11;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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