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Mortality Options: the Point of View of an Insurer

Author

Listed:
  • Schmeck, Maren Diane

    (Center for Mathematical Economics, Bielefeld University)

  • Schmidli, Hanspeter

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We consider the surplus process of a life insurer who is able to buy a securitisation product to hedge mortality in a discrete time framework. Two cohorts are considered: one underlying the securitisation product and one for the portfolio of the insurer. In our main result we show that there exists a unique strategy that maximises the expected utility of the insurer. Our findings are illustrated by a tractable model for mortality catastrophe risk.

Suggested Citation

  • Schmeck, Maren Diane & Schmidli, Hanspeter, 2019. "Mortality Options: the Point of View of an Insurer," Center for Mathematical Economics Working Papers 616, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:616
    as

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    File URL: https://pub.uni-bielefeld.de/download/2935798/2935799
    File Function: First Version, 2019
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    References listed on IDEAS

    as
    1. Delong, Lukasz & Gerrard, Russell & Haberman, Steven, 2008. "Mean-variance optimization problems for an accumulation phase in a defined benefit plan," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 107-118, February.
    2. Bauer, Daniel & Börger, Matthias & Ruß, Jochen, 2010. "On the pricing of longevity-linked securities," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 139-149, February.
    3. David Blake & Andrew Cairns & Kevin Dowd & Richard MacMinn, 2006. "Longevity Bonds: Financial Engineering, Valuation, and Hedging," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 647-672, December.
    4. Menoncin, Francesco, 2008. "The role of longevity bonds in optimal portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 343-358, February.
    5. Schmock, Uwe, 1999. "Estimating the Value of the Wincat Coupons of the Winterthur Insurance Convertible Bond: A Study of the Model Risk1," ASTIN Bulletin, Cambridge University Press, vol. 29(1), pages 101-163, May.
    6. Paolo Battocchio & Francesco Menoncin & Olivier Scaillet, 2007. "Optimal asset allocation for pension funds under mortality risk during the accumulation and decumulation phases," Annals of Operations Research, Springer, vol. 152(1), pages 141-165, July.
    7. Cox, Samuel H. & Fairchild, Joseph R. & Pedersen, Hal W., 2000. "Economic Aspects of Securitization of Risk," ASTIN Bulletin, Cambridge University Press, vol. 30(1), pages 157-193, May.
    8. 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.
    9. repec:eee:insuma:v:76:y:2017:i:c:p:75-86 is not listed on IDEAS
    10. Stéphane Loisel, 2010. "Understanding, Modeling and Managing Longevity Risk: Key Issues and Main Challenges," Post-Print hal-00517902, HAL.
    11. Christensen, Claus Vorm & Schmidli, Hanspeter, 2000. "Pricing catastrophe insurance products based on actually reported claims," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 189-200, October.
    12. repec:taf:uaajxx:v:4:y:2000:i:4:p:56-82 is not listed on IDEAS
    13. 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.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    mortality option; optimal strategy; maximal utility; ex- ponential utility;

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