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Benchmark-Neutral Risk-Minimization for insurance products and nonreplicable claims

Author

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  • Michael Schmutz
  • Eckhard Platen
  • Thorsten Schmidt

Abstract

In this paper we study the pricing and hedging of nonreplicable contingent claims, such as long-term insurance contracts like variable annuities. Our approach is based on the benchmark-neutral pricing framework of Platen (2024), which differs from the classical benchmark approach by using the stock growth optimal portfolio as the num\'eraire. In typical settings, this choice leads to an equivalent martingale measure, the benchmark-neutral measure. The resulting prices can be significantly lower than the respective risk-neutral ones, making this approach attractive for long-term risk-management. We derive the associated risk-minimizing hedging strategy under the assumption that the contingent claim possesses a martingale decomposition. For a set of nonreplicable contingent claims, these strategies allow monitoring the working capital required to generate their payoffs and enable an assessment of the resulting diversification effects. Furthermore, an algorithmic refinancing strategy is proposed that allows modeling the working capital. Finally, insurance-finance arbitrages of the first kind are introduced and it is demonstrated that benchmark-neutral pricing effectively avoids such arbitrages.

Suggested Citation

  • Michael Schmutz & Eckhard Platen & Thorsten Schmidt, 2025. "Benchmark-Neutral Risk-Minimization for insurance products and nonreplicable claims," Papers 2506.19494, arXiv.org.
    • Handle: RePEc:arx:papers:2506.19494
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    References listed on IDEAS

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    1. Rüdiger Frey & Thorsten Schmidt, 2012. "Pricing and hedging of credit derivatives via the innovations approach to nonlinear filtering," Finance and Stochastics, Springer, vol. 16(1), pages 105-133, January.
    2. Thorsten Schmidt & Alexander Novikov, 2008. "A Structural Model with Unobserved Default Boundary," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 183-203.
    3. Leland, Hayne E & Toft, Klaus Bjerre, 1996. "Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Journal of Finance, American Finance Association, vol. 51(3), pages 987-1019, July.
    4. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    5. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496, December.
    6. Eckhard Platen, 2024. "Benchmark-Neutral Pricing," Papers 2407.01542, arXiv.org.
    7. Eckhard Platen & David Heath, 2006. "A Benchmark Approach to Quantitative Finance," Springer Finance, Springer, number 978-3-540-47856-0, March.
    8. Laura Ballotta & Ernst Eberlein & Thorsten Schmidt & Raghid Zeineddine, 2020. "Variable annuities in a Lévy-based hybrid model with surrender risk," Quantitative Finance, Taylor & Francis Journals, vol. 20(5), pages 867-886, May.
    9. Ballotta, Laura & Eberlein, Ernst & Schmidt, Thorsten & Zeineddine, Raghid, 2021. "Fourier based methods for the management of complex life insurance products," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 320-341.
    10. Eckhard Platen & Renata Rendek, 2020. "Approximating The Growth Optimal Portfolio And Stock Price Bubbles," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(07), pages 1-33, November.
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    Cited by:

    1. Eckhard Platen, 2025. "Information-minimizing stationary financial market dynamics," Papers 2507.18395, arXiv.org.
    2. Eckhard Platen, 2026. "Information-Theoretic Approach to Financial Market Modelling," Papers 2602.14575, arXiv.org.

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