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Annuitizing at a bounded, absolutely continuous rate to minimize the probability of lifetime ruin

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  • Liang, Xiaoqing
  • Young, Virginia R.

Abstract

We minimize the probability of lifetime ruin in a deterministic financial and insurance model, although the investor's time of death is random, with an age-dependent force of mortality. By contrast with the traditional anything-anytime annuitization model (that is, individuals can annuitize any fraction of their wealth at anytime), the individual only purchases life annuity income gradually, using a bounded, absolutely continuous rate. As in the anything-anytime annuitization case, we find that it is optimal for the individual not to purchase additional annuity income when her wealth is less than a specific linear function of her existing annuity income, which we call the buy boundary. Interestingly, we find the buy boundary in our model is identical to the one in the anything-anytime annuitization model. However, there is a separate threshold, which we call the safe level. (This threshold degenerates to the buy boundary in the anything-anytime annuitization model.) When wealth is greater than the safe level, the minimum probability of lifetime ruin is zero; when wealth lies between the buy boundary and the safe level, the individual's best choice is to purchase annuity income at the maximum allowable rate.

Suggested Citation

  • Liang, Xiaoqing & Young, Virginia R., 2023. "Annuitizing at a bounded, absolutely continuous rate to minimize the probability of lifetime ruin," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 80-96.
    • Handle: RePEc:eee:insuma:v:112:y:2023:i:c:p:80-96
    DOI: 10.1016/j.insmatheco.2023.06.003
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    References listed on IDEAS

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    1. Jeffrey R. Brown & Jeffrey R. Kling & Sendhil Mullainathan & Marian V. Wrobel, 2008. "Why Don’t People Insure Late-Life Consumption? A Framing Explanation of the Under-Annuitization Puzzle," American Economic Review, American Economic Association, vol. 98(2), pages 304-309, May.
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    More about this item

    Keywords

    Probability of lifetime ruin; Optimal annuitization; Absolutely continuous annuitization rate; Barrier strategy; Age-dependent force of mortality;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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