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Risk-neutral valuation of GLWB riders in variable annuities

Author

Listed:
  • Bacinello, Anna Rita
  • Maggistro, Rosario
  • Zoccolan, Ivan

Abstract

In this paper we propose a model for pricing GLWB variable annuities under a stochastic mortality framework. Our set-up is very general and only requires the Markovian property for the mortality intensity and the asset price processes. The contract value is defined through an optimization problem which is solved by using dynamic programming. We prove, by backward induction, the validity of the bang-bang condition for the set of discrete withdrawal strategies of the model. This result is particularly remarkable as in the insurance literature either the existence of optimal bang-bang controls is assumed or it requires suitable conditions. We assume constant interest rates, although our results still hold in the case of a Markovian interest rate process. We present extensive numerical examples, modelling the mortality intensity as a non mean reverting square root process and the asset price as an exponential Lévy process, and compare the results obtained for different parameters and policyholder behaviours.

Suggested Citation

  • Bacinello, Anna Rita & Maggistro, Rosario & Zoccolan, Ivan, 2024. "Risk-neutral valuation of GLWB riders in variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 1-14.
    • Handle: RePEc:eee:insuma:v:114:y:2024:i:c:p:1-14
    DOI: 10.1016/j.insmatheco.2023.10.001
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    References listed on IDEAS

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    More about this item

    Keywords

    GLWB; Dynamic withdrawals; Bang-bang condition; Lévy processes; Stochastic mortality;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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