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Risk-minimizing hedging strategies for insurance payment processes

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  • Thomas Møller

    (Laboratory of Actuarial Mathematics, Institute for Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark Manuscript)

Abstract

Föllmer and Sondermann (1986) proved the existence of a unique admissible risk-minimizing hedging strategy for any square-integrable contingent claim H in the martingale case. We extend this approach to the situation where the hedger's liabilities are described by a general payment process A and consider some examples related to insurance. These include a general unit-linked life insurance contract driven by a Markov jump process and a claim process from non-life insurance where the claim size distribution is affected by a traded price index.

Suggested Citation

  • Thomas Møller, 2001. "Risk-minimizing hedging strategies for insurance payment processes," Finance and Stochastics, Springer, vol. 5(4), pages 419-446.
    • Handle: RePEc:spr:finsto:v:5:y:2001:i:4:p:419-446
    Note: received: November 1998; final version received: October 2000
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    References listed on IDEAS

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    7. Schweizer, Martin, 1999. "A guided tour through quadratic hedging approaches," SFB 373 Discussion Papers 1999,96, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    Citations

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    Cited by:

    1. Vandaele, Nele & Vanmaele, Michèle, 2008. "A locally risk-minimizing hedging strategy for unit-linked life insurance contracts in a Lévy process financial market," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1128-1137, June.
    2. Coleman, Thomas F. & Li, Yuying & Patron, Maria-Cristina, 2006. "Hedging guarantees in variable annuities under both equity and interest rate risks," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 215-228, April.
    3. Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2014. "A benchmark approach to risk-minimization under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 129-146.
    4. 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.
    5. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Riesner, Martin, 2006. "Hedging life insurance contracts in a Lévy process financial market," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 599-608, June.
    7. 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.
    8. Hambel, Christoph & Kraft, Holger & Meyer-Wehmann, André, 2023. "When should retirees tap their home equity?," Journal of Banking & Finance, Elsevier, vol. 154(C).
    9. Barbarin, Jérôme, 2008. "Heath-Jarrow-Morton modelling of longevity bonds and the risk minimization of life insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 41-55, August.
    10. Fischer, Tom, 2007. "A law of large numbers approach to valuation in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 35-57, January.
    11. Pansera, Jérôme, 2012. "Discrete-time local risk minimization of payment processes and applications to equity-linked life-insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 1-11.
    12. Dirk Becherer & Martin Schweizer, 2005. "Classical solutions to reaction-diffusion systems for hedging problems with interacting Ito and point processes," Papers math/0505208, arXiv.org.
    13. Jaimungal, Sebastian & Young, Virginia R., 2005. "Pricing equity-linked pure endowments with risky assets that follow Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 329-346, June.
    14. Delong, Lukasz, 2010. "An optimal investment strategy for a stream of liabilities generated by a step process in a financial market driven by a Lévy process," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 278-293, December.
    15. Jacek Jakubowski & Mariusz Niewk{e}g{l}owski, 2013. "Risk-minimization and hedging claims on a jump-diffusion market model, Feynman-Kac Theorem and PIDE," Papers 1305.4132, arXiv.org, revised Jul 2013.

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    More about this item

    Keywords

    Risk-minimization; incomplete market; payment streams; unit-linked life insurance; marked point process;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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