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Uniqueness of equilibrium with survival probability heterogeneity and endogenous annuity price

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  • Lau, Sau-Him Paul
  • Ying, Yinan
  • Zhang, Qilin

Abstract

When annuitants' survival probabilities are heterogeneous, the equilibrium annuity price is affected by their annuitization choices, which further depend on the annuity price. Given this mutual dependence, it is generally difficult to establish uniqueness of the equilibrium. Based on similar expressions appearing in several annuity and insurance models, we obtain two results in an annuity model with heterogeneity in survival probability only. First, the equilibrium annuity price is always unique if the annuitization function is multiplicatively separable in survival probability and annuity price. Second, the equilibrium is unique for more general annuitization functions, provided that a sufficient condition on the distribution of survival probabilities holds. Many distributions, including the uniform, normal and gamma distributions, satisfy this condition.

Suggested Citation

  • Lau, Sau-Him Paul & Ying, Yinan & Zhang, Qilin, 2024. "Uniqueness of equilibrium with survival probability heterogeneity and endogenous annuity price," Insurance: Mathematics and Economics, Elsevier, vol. 119(C), pages 146-156.
    • Handle: RePEc:eee:insuma:v:119:y:2024:i:c:p:146-156
    DOI: 10.1016/j.insmatheco.2024.08.004
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    Cited by:

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    More about this item

    Keywords

    Survival probability heterogeneity; Annuitization choices; Annuity price; Mutual dependence; Uniqueness of equilibrium;
    All these keywords.

    JEL classification:

    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving
    • G52 - Financial Economics - - Household Finance - - - Insurance

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