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Optimal investment-withdrawal strategy for variable annuities under a performance fee structure

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  • Feng, Runhuan
  • Jing, Xiaochen
  • Ng, Kenneth Tsz Hin

Abstract

Variable Annuities (VAs) provide policyholders with market participation while offering additional protection from insurers. In this article, we develop a mathematical model to explore the impact of different fee structures on VAs with a ratchet feature and derive analytical solutions to the associated optimal investment-withdrawal problem. We focus on a performance fee structure, highlighting its advantages over the traditional constant fee structure from both the insurer's and policyholder's perspectives. Our findings show that policyholders adopt more conservative investment strategies under the performance fee, leading to increased expected profits and reduced tail risks for risk-neutral insurers. From a mathematical standpoint, we contribute by proving the well-posedness of the associated free-boundary value problems (FBPs) and establishing verification theorems for the underlying control problems. These results involve non-standard analysis and estimations due to the ratchet feature and the guaranteed protections embedded in the contract.

Suggested Citation

  • Feng, Runhuan & Jing, Xiaochen & Ng, Kenneth Tsz Hin, 2025. "Optimal investment-withdrawal strategy for variable annuities under a performance fee structure," Journal of Economic Dynamics and Control, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:dyncon:v:170:y:2025:i:c:s0165188924001957
    DOI: 10.1016/j.jedc.2024.105003
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    References listed on IDEAS

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    More about this item

    Keywords

    Variable annuities; Ratchet benefit; Fee structure; Verification theorem; Optimal investment-withdrawal strategies;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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