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HEDGING MORTALITY CLAIMS WITH LONGEVITY BONDS*

Published online by Cambridge University Press:  18 June 2013

Francesca Biagini ,
Thorsten Rheinländer  and
Jan Widenmann
Francesca Biagini
Affiliation:
Department of Mathematics, LMU Munich, Theresienstr. 39, 80333 Munich, Germany E-Mail: francesca.biagini@math.lmu.de
Thorsten Rheinländer*
Affiliation:
Research Group Financial and Actuarial Mathematics, Vienna University of Technology, Wiedner Hauptstrasse 8-10/E105, A-1040 Vienna, Austria
Jan Widenmann
Affiliation:
Department of Mathematics, LMU Munich, Theresienstr. 39, 80333 Munich, Germany E-Mail: jan.widenmann@math.lmu.de
*
E-Mail: rheinlan@fam.tuwien.ac.at
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Abstract

We study mean–variance hedging of a pure endowment, a term insurance and general annuities by trading in a longevity bond with continuous rate payments proportional to the survival probability. In particular, we discuss the introduction of a gratification annuity as an interesting insurance product for the life insurance market. The optimal hedging strategies are determined via their Galtchouk–Kunita–Watanabe decompositions under specific, yet sufficiently general model assumptions. The results are then further illustrated by assuming a general affine structure of the mortality intensity process. The optimal hedging strategies as well as the residual hedging error of a gratification annuity and a simple life annuity are finally investigated with numerical simulations, which illustrate the nice features of the gratification annuity for the insurance industry.

Keywords

Mean-variance hedginglife insurancelongevity bondintensity-based approachaffine mortality intensity
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 43 , Issue 2 , May 2013 , pp. 123 - 157
Copyright
Copyright © ASTIN Bulletin 2013 

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Footnotes

*

The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. (228087).

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