Uniqueness of equilibrium when the annuity payout level and annuitization choices are mutually dependent

Sau-Him Paul LAU*, Yinan YING, Qilin ZHANG

*Corresponding author for this work

Research output: Working paperPreprint

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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 and normal distributions, satisfy this condition.
Original languageEnglish
Publication statusSubmitted - 1 Nov 2023

Bibliographical note

Preprint uploaded by author - YING Yinan (12 April 2024)

Keywords

  • Annuity price
  • Uniqueness of equilibrium
  • Health heterogeneity
  • Mutual dependence

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