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Life insurance policies with cash flows subject to random interest rate changes

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  • David R. Ba~nos

Abstract

The main purpose of this work is to derive a partial differential equation for the reserves of life insurance liabilities subject to stochastic interest rates where the benefits and premiums depend directly on changes in the interest rate curve. In particular, we allow the payment streams to depend on the performance of an overnight technical interest rate, making them stochastic as well. This opens up for considering new types of contracts based on the performance of the insurer's returns on their own investments. We provide explicit solutions for the reserves when the premiums and benefits vary according to interest rate levels or averages under the Vasicek model and conduct some simulations computing reserve surfaces numerically. We also give an example of a reinsurance treaty taking over pension payments when the insurer's average returns fall under some specified threshold.

Suggested Citation

  • David R. Ba~nos, 2020. "Life insurance policies with cash flows subject to random interest rate changes," Papers 2012.15541, arXiv.org.
    • Handle: RePEc:arx:papers:2012.15541
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    References listed on IDEAS

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    1. Aase Nielsen, J. & Sandmann, Klaus, 1995. "Equity-linked life insurance: A model with stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 16(3), pages 225-253, July.
    2. David R. Ba~nos & Marc Lagunas-Merino & Salvador Ortiz-Latorre, 2020. "Variance and interest rate risk in unit-linked insurance policies," Papers 2006.14833, arXiv.org.
    3. J. Aase Nielsen & Klaus Sandmann, 1996. "Uniqueness of the Fair Premium for Equity-Linked Life Insurance Contracts," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 21(1), pages 65-102, June.
    4. David Baños & Marc Lagunas-Merino & Salvador Ortiz-Latorre, 2020. "Variance and Interest Rate Risk in Unit-Linked Insurance Policies," Risks, MDPI, vol. 8(3), pages 1-23, August.
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