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Risk Minimization for Insurance Products via F-Doubly Stochastic Markov Chains

Author

Listed:
  • Francesca Biagini

    (Department of Mathematics, University of Munich, Theresienstraße 39, 80333 Munich, Germany
    Department of Mathematics, University of Oslo, Boks 1072 Blindern, Norway)

  • Andreas Groll

    (Department of Statistics, University of Munich, Akademiestr.1, 80799 Munich, Germany)

  • Jan Widenmann

    (BMW Financial Services, BMW Bank GmbH, 80787 Munich, Germany)

Abstract

We study risk-minimization for a large class of insurance contracts. Given that the individual progress in time of visiting an insurance policy’s states follows an F -doubly stochastic Markov chain, we describe different state-dependent types of insurance benefits. These cover single payments at maturity, annuity-type payments and payments at the time of a transition. Based on the intensity of the F -doubly stochastic Markov chain, we provide the Galtchouk-Kunita-Watanabe decomposition for a general insurance contract and specify risk-minimizing strategies in a Brownian financial market setting. The results are further illustrated explicitly within an affine structure for the intensity.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jrisks:v:4:y:2016:i:3:p:23-:d:73446
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    References listed on IDEAS

    as
    1. Ragnar Norberg, 1999. "A theory of bonus in life insurance," Finance and Stochastics, Springer, vol. 3(4), pages 373-390.
    2. Francesca Biagini & Alessandra Cretarola & Eckhard Platen, 2012. "Local Risk-Minimization under the Benchmark Approach," Research Paper Series 319, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    4. Biagini, Francesca & Rheinländer, Thorsten & Widenmann, Jan, 2013. "Hedging Mortality Claims With Longevity Bonds," ASTIN Bulletin, Cambridge University Press, vol. 43(2), pages 123-157, May.
    5. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    6. Ragnar Norberg, 2013. "Optimal hedging of demographic risk in life insurance," Finance and Stochastics, Springer, vol. 17(1), pages 197-222, January.
    7. Blake David & Cairns Andrew & Dowd Kevin, 2008. "The Birth of the Life Market," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 3(1), pages 1-32, September.
    8. Biagini, Francesca & Groll, Andreas & Widenmann, Jan, 2013. "Intensity-based premium evaluation for unemployment insurance products," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 302-316.
    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. LUCIANO, Elisa & VIGNA, Elena, 2008. "Mortality risk via affine stochastic intensities: calibration and empirical relevance," MPRA Paper 59627, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    insurance liabilities; doubly stochastic Markov chains; risk minimization; MSC; 60J27; 62P05; 91G99; JEL; C02;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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