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A Comparative Study of Risk Measures for Guaranteed Minimum Maturity Benefits by a PDE Method

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  • Runhuan Feng

Abstract

The stochastic modeling and determination of reserves and risk capitals for variable annuity guarantee products are relatively new developments in the insurance industry. The current market practice is largely based on Monte Carlo simulations, which have great engineering flexibility, but the demand for heavy computational power can be prohibitive in many cases. In this article we distinguish and compare two types of risk models to determine the commonly used risk measures for reserving and capital calculations. Using an example of the guaranteed minimum maturity benefit, we investigate alternative numerical methods that require less computational resources and yet achieve high accuracy and efficiency.

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  • Runhuan Feng, 2014. "A Comparative Study of Risk Measures for Guaranteed Minimum Maturity Benefits by a PDE Method," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(4), pages 445-461, October.
    • Handle: RePEc:taf:uaajxx:v:18:y:2014:i:4:p:445-461
    DOI: 10.1080/10920277.2014.922031
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    Cited by:

    1. Feng, Runhuan & Huang, Huaxiong, 2016. "Statutory financial reporting for variable annuity guaranteed death benefits: Market practice, mathematical modeling and computation," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 54-64.
    2. Feng, Runhuan & Shimizu, Yasutaka, 2016. "Applications of central limit theorems for equity-linked insurance," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 138-148.
    3. Runhuan Feng & Hans W. Volkmer, 2015. "Conditional Asian Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1-24.
    4. Runhuan Feng & Xiaochen Jing & Jan Dhaene, 2015. "Comonotonic Approximations of Risk Measures for Variable Annuity Guaranteed Benefits with Dynamic Policyholder Behavior," Tinbergen Institute Discussion Papers 15-008/IV/DSF85, Tinbergen Institute.
    5. Feng, Runhuan & Yi, Bingji, 2019. "Quantitative modeling of risk management strategies: Stochastic reserving and hedging of variable annuity guaranteed benefits," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 60-73.
    6. Wenlong Hu, 2020. "Risk management of guaranteed minimum maturity benefits under stochastic mortality and regime-switching by Fourier space time-stepping framework," Papers 2006.15483, arXiv.org, revised Dec 2020.
    7. Huang, Yiming & Mamon, Rogemar & Xiong, Heng, 2022. "Valuing guaranteed minimum accumulation benefits by a change of numéraire approach," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 1-26.
    8. Kouritzin, Michael A. & MacKay, Anne, 2018. "VIX-linked fees for GMWBs via explicit solution simulation methods," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 1-17.
    9. Maciej Augustyniak & Mathieu Boudreault, 2017. "Mitigating Interest Rate Risk in Variable Annuities: An Analysis of Hedging Effectiveness under Model Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(4), pages 502-525, October.
    10. Runhuan Feng & Hans W. Volkmer, 2015. "Conditional Asian Options," Papers 1505.06946, arXiv.org.

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