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Max–Min Optimization Problem For Variable Annuities Pricing

Author

Listed:
  • CHRISTOPHETTE BLANCHET-SCALLIET

    (Institut Camille Jordan, Université de Lyon, Ecole Centrale de Lyon, CNRS UMR 5208 Ecully, France)

  • ETIENNE CHEVALIER

    (LaMME, Université d’Evry Val d’Essonne, UMR CNRS 8071, Evry, France)

  • IDRIS KHARROUBI

    (CEREMADE, Université Paris Dauphine, CNRS UMR 7534, Crest, Paris, France)

  • THOMAS LIM

    (LaMME, ENSIIE, UMR CNRS 8071 Evry, France)

Abstract

In this paper, we study the valuation of variable annuities for an insurer. We concentrate on two types of these contracts, namely guaranteed minimum death benefits and guaranteed minimum living benefits that allow the insured to withdraw money from the associated account. Here, the price of variable annuities corresponds to a fee, fixed at the beginning of the contract, that is continuously taken from the associated account. We use a utility indifference approach to determine the indifference fee rate. We focus on the worst case for the insurer, assuming that the insured makes the withdrawals that minimize the expected utility of the insurer. To compute this indifference fee rate, we link the utility maximization in the worst case for the insurer to a sequence of maximization and minimization problems that can be computed recursively. This allows to provide an optimal investment strategy for the insurer when the insured follows the worst withdrawal strategy and to compute the indifference fee. We finally explain how to approximate these quantities via the previous results and give numerical illustrations of parameter sensitivity.

Suggested Citation

  • Christophette Blanchet-Scalliet & Etienne Chevalier & Idris Kharroubi & Thomas Lim, 2015. "Max–Min Optimization Problem For Variable Annuities Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-35, December.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:08:n:s0219024915500533
    DOI: 10.1142/S0219024915500533
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    References listed on IDEAS

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    1. A. C. Belanger & P. A. Forsyth & G. Labahn, 2009. "Valuing the Guaranteed Minimum Death Benefit Clause with Partial Withdrawals," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(6), pages 451-496.
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    Cited by:

    1. Huansang Xu & Ruyi Liu & Marek Rutkowski, 2023. "Equity Protection Swaps: A New Type of Investment Insurance for Holders of Superannuation Accounts," Papers 2305.09472, arXiv.org, revised Apr 2024.

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