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Mathematics and Financial Economics

, Volume 10, Issue 2, pp 151–178 | Cite as

Risk-minimization for life insurance liabilities with basis risk

  • Francesca BiaginiEmail author
  • Thorsten Rheinländer
  • Irene Schreiber
Article

Abstract

In this paper we study the hedging of typical life insurance payment processes in a general setting by means of the well-known risk-minimization approach. We find the optimal risk-minimizing strategy in a financial market where we allow for investments in a hedging instrument based on a longevity index, representing the systematic mortality risk. Thereby we take into account and model the basis risk that arises due to the fact that the insurance company cannot perfectly hedge its exposure by investing in a hedging instrument that is based on the longevity index, not on the insurance portfolio itself. We also provide a detailed example within the context of unit-linked life insurance products where the dependency between the index and the insurance portfolio is described by means of an affine mean-reverting diffusion process with stochastic drift.

Keywords

Life insurance payment processes Risk-minimization  Martingale representation Basis risk Affine mortality structure 

Mathematics Subject Classification

62P05 91G80 91G20 62P20 

JEL Classification

C02  G19  G10 

Notes

Acknowledgments

We wish to thank an anonymous referee for advices and remarks, which contributed to improve the paper.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Francesca Biagini
    • 1
    Email author
  • Thorsten Rheinländer
    • 2
  • Irene Schreiber
    • 3
  1. 1.Department of MathematicsUniversity of MunichMunichGermany
  2. 2.Financial and Actuarial Mathematics GroupVienna University of TechnologyViennaAustria
  3. 3.MunichGermany

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