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Natural hedging in continuous time life insurance

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Abstract

Life insurance companies face several types of risks including financial risks and insurance risks. Financial risks can to a large extent be hedged by trading in the financial market, but there exists no such market for insurance risks. We suggest an alternative to hedge insurance risks. In a multi-state setup in continuous time life insurance, we describe the concept of natural hedging, which enables us to compose a portfolio of different insurance products where the liabilities are unaffected by shifts in the transition intensities. We describe how to find and how to calculate the natural hedging strategy using directional derivatives (Gateaux derivatives) to measure the sensitivity of the life insurance liabilities with respect to shifts in the transition intensities of a Markov chain governing the state of the insured. Furthermore, we implement the natural hedging strategy in two numerical examples based on the survival model and the disability model, respectively.

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Acknowledgements

The author would like to thank an anonymous referee whose comments have been very helpful to improve a previous version of the present work.

Funding

This research was funded by Innovation Fund Denmark award number 7076-00029.

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Authors and Affiliations

  1. Department of Mathematical Science, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark

    Anna Kamille Nyegaard

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  1. Anna Kamille Nyegaard
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Correspondence to Anna Kamille Nyegaard.

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Nyegaard, A.K. Natural hedging in continuous time life insurance. Eur. Actuar. J. 13, 497–515 (2023). https://doi.org/10.1007/s13385-022-00340-2

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  • DOI: https://doi.org/10.1007/s13385-022-00340-2

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