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Optimal fee structure of variable annuities

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  • Wang, Gu
  • Zou, Bin

Abstract

We study the design of fee structures of variable annuities as a stochastic control problem, in which an insurer is allowed to choose the fee structure in any form that satisfies the budget constraint, and seeks an optimal one to maximize its business objective. Under the no surrender assumption, we show that the optimal fee structure is of barrier type with a time-dependent free boundary. The insurer's optimal strategy is to charge fees if and only if the account value of variable annuities hits the free boundary from below.

Suggested Citation

  • Wang, Gu & Zou, Bin, 2021. "Optimal fee structure of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 587-601.
    • Handle: RePEc:eee:insuma:v:101:y:2021:i:pb:p:587-601
    DOI: 10.1016/j.insmatheco.2021.10.003
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    References listed on IDEAS

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    Cited by:

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    2. Cao, Jingyi & Li, Dongchen & Young, Virginia R. & Zou, Bin, 2022. "Stackelberg differential game for insurance under model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 128-145.

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    More about this item

    Keywords

    Barrier strategy; Free boundary; Hamilton-Jacobi-Bellman equation; Quasi-variational inequalities; Reflected stochastic differential equations;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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