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Optimal consumption and allocation in variable annuities with Guaranteed Minimum Death Benefits

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  • Gao, Jin
  • Ulm, Eric R.

Abstract

We determine the optimal allocation of funds between the fixed and variable subaccounts in a variable annuity with a GMDB (Guaranteed Minimum Death Benefit) clause featuring partial withdrawals by using a utility-based approach. The Merton method is applied by assuming that individuals allocate funds optimally in order to maximize the expected utility of lifetime consumption. It also reflects bequest motives by including the recipient’s utility in terms of the policyholder’s guaranteed death benefits. We derive the optimal transfer choice by the insured, and furthermore price the GMDB through maximizing the discounted expected utility of the policyholders and beneficiaries by investing dynamically in the fixed account and variable fund and withdrawing optimally.

Suggested Citation

  • Gao, Jin & Ulm, Eric R., 2012. "Optimal consumption and allocation in variable annuities with Guaranteed Minimum Death Benefits," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 586-598.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:3:p:586-598
    DOI: 10.1016/j.insmatheco.2012.08.003
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    Cited by:

    1. Xu, Wei & Chen, Yuehuan & Coleman, Conrad & Coleman, Thomas F., 2018. "Moment matching machine learning methods for risk management of large variable annuity portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 1-20.
    2. Yung-Tsung Lee & Tianxiang Shi, 2022. "Valuation of Reverse Mortgages with Surrender: A Utility Approach," The Journal of Real Estate Finance and Economics, Springer, vol. 65(4), pages 593-621, November.
    3. Horneff, Vanya & Maurer, Raimond & Mitchell, Olivia S. & Rogalla, Ralph, 2015. "Optimal life cycle portfolio choice with variable annuities offering liquidity and investment downside protection," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 91-107.
    4. Ulm, Eric, 2020. "Analytic Valuation of GMDB Options with Utility Based Asset Allocation," Working Paper Series 21060, Victoria University of Wellington, School of Economics and Finance.
    5. Kevin Maritato & Morton Lane & Matthew Murphy & Stan Uryasev, 2022. "Optimal Allocation of Retirement Portfolios," JRFM, MDPI, vol. 15(2), pages 1-17, February.
    6. Gao, Jin & Ulm, Eric R., 2015. "Optimal allocation and consumption with guaranteed minimum death benefits, external income and term life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 87-98.
    7. Gan, Guojun & Lin, X. Sheldon, 2015. "Valuation of large variable annuity portfolios under nested simulation: A functional data approach," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 138-150.
    8. Wang, Yayun & Zhang, Zhimin & Yu, Wenguang, 2021. "Pricing equity-linked death benefits by complex Fourier series expansion in a regime-switching jump diffusion model," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    9. Gan, Guojun, 2013. "Application of data clustering and machine learning in variable annuity valuation," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 795-801.
    10. Huang, H. & Milevsky, M.A. & Salisbury, T.S., 2014. "Optimal initiation of a GLWB in a variable annuity: No Arbitrage approach," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 102-111.
    11. Steinorth, Petra & Mitchell, Olivia S., 2015. "Valuing variable annuities with guaranteed minimum lifetime withdrawal benefits," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 246-258.
    12. Tang, Chun-Hua, 2018. "Subjective value of the guarantees embedded in public cash-balance pension plans," Journal of Pension Economics and Finance, Cambridge University Press, vol. 17(2), pages 231-250, April.
    13. Ulm, Eric, 2020. "Analytic Valuation of GMDB Options with Utility Based Asset Allocation," Working Paper Series 8566, Victoria University of Wellington, School of Economics and Finance.
    14. Moenig, Thorsten, 2021. "Variable annuities: Market incompleteness and policyholder behavior," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 63-78.
    15. Dong, Bing & Xu, Wei & Sevic, Aleksandar & Sevic, Zeljko, 2020. "Efficient willow tree method for variable annuities valuation and risk management☆," International Review of Financial Analysis, Elsevier, vol. 68(C).
    16. Thorsten Moenig, 2021. "Efficient valuation of variable annuity portfolios with dynamic programming," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(4), pages 1023-1055, December.
    17. Anne Mackay & Marie-Claude Vachon, 2023. "On an Optimal Stopping Problem with a Discontinuous Reward," Papers 2311.03538, arXiv.org, revised Nov 2023.
    18. Pavel V. Shevchenko & Xiaolin Luo, 2016. "A Unified Pricing of Variable Annuity Guarantees under the Optimal Stochastic Control Framework," Risks, MDPI, vol. 4(3), pages 1-31, July.
    19. Pavel V. Shevchenko & Xiaolin Luo, 2016. "A unified pricing of variable annuity guarantees under the optimal stochastic control framework," Papers 1605.00339, arXiv.org.

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    More about this item

    Keywords

    GMDB; Variable annuity; Merton model; Expected utility;
    All these keywords.

    JEL classification:

    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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