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Optimal hedging of demographic risk in life insurance

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.

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References

  1. Cairns, A.J.G., Blake, D., Dowd, K.: Pricing death: frameworks for the valuation and securitization of mortality risk. ASTIN Bull. 36, 79–120 (2006)

    MathSciNet  MATH  Article  Google Scholar 

  2. Cairns, A.J.G., Blake, D., Dowd, K.: Modelling and management of mortality risk: an overview. Scand. Actuar. J. 2008, 70–113 (2008)

    MathSciNet  Article  Google Scholar 

  3. Dahl, M.: Stochastic mortality in life insurance: market reserves and mortality linked insurance contracts. Insur. Math. Econ. 35, 113–136 (2004)

    MathSciNet  MATH  Article  Google Scholar 

  4. Dahl, M., Møller, T.: Valuation and hedging of life insurance liabilities with systematic mortality risk. Insur. Math. Econ. 39, 193–217 (2006)

    MATH  Article  Google Scholar 

  5. Dahl, M., Melchior, M., Møller, T.: On systematic mortality risk and risk-minimization with survivor swaps. Scand. Actuar. J. 2008, 114–146 (2008)

    MATH  Article  Google Scholar 

  6. Föllmer, H., Schied, A.: Stochastic Finance, 3rd edn. De Gruyter, Berlin (2011)

    Google Scholar 

  7. Karr, A.: Point Processes and Their Statistical Inference, 2nd edn. Dekker, New York (1991)

    MATH  Google Scholar 

  8. Møller, T.: Risk-minimizing hedging strategies for insurance payment processes. Finance Stoch. 5, 419–446 (2001)

    MathSciNet  Article  Google Scholar 

  9. Møller, T., Steffensen, M.: Market-Valuation Methods in Life and Pension Insurance. Cambridge University Press, Cambridge (2007)

    Book  Google Scholar 

  10. Norberg, R.: A theory of bonus in life insurance. Finance Stoch. 3, 373–390 (1999)

    MathSciNet  MATH  Article  Google Scholar 

  11. Norberg, R.: The Markov chain market. ASTIN Bull. 33, 265–287 (2003)

    MathSciNet  MATH  Article  Google Scholar 

  12. Norberg, R.: The pension crisis: its causes, possible remedies, and the role of the regulator. In: Erfaringer og utfordringer, 20 years Jubilee Volume of Kredittilsynet. Kredittilsynet, the Financial Supervisory Authority of Norway, Oslo (2006)

    Google Scholar 

  13. Norberg, R.: Quadratic hedging of payment streams. Working paper, http://isfa.univ-lyon1.fr/~norberg (2012)

  14. Rao, C.R.: Linear Statistical Inference and Its Application, 2nd edn. Wiley, New York (1973)

    Book  Google Scholar 

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Acknowledgements

The author thanks the BNP Paribas Insurance Chair “Management de la modélisation” for financial support. The views expressed in this document are the author’s own and do not necessarily reflect those endorsed by BNP Paribas Insurance. Thanks are also due to referees and editors whose general comments as well as attention to details were helpful.

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Correspondence to Ragnar Norberg.

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Norberg, R. Optimal hedging of demographic risk in life insurance. Finance Stoch 17, 197–222 (2013). https://doi.org/10.1007/s00780-012-0182-3

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  • DOI: https://doi.org/10.1007/s00780-012-0182-3

Keywords

  • Stochastic mortality
  • Mortality derivatives
  • Mean-variance hedging
  • Optimal design of derivatives

Mathematics Subject Classification

  • 60G55
  • 62P05
  • 91B30
  • 91G20

JEL Classification

  • C02
  • G11