Uniqueness of equilibrium with survival probability heterogeneity and endogenous annuity price

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

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

1 Citation (Scopus)
35 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)146-156
Number of pages11
JournalInsurance: Mathematics and Economics
Volume119
Early online date30 Aug 2024
DOIs
Publication statusPublished - Nov 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier B.V.

Funding

We are grateful to two reviewers and Kelvin Yuen for very helpful comments and suggestions, and to Yiwen Zhao for research assistance. We thank the Research Grants Council of Hong Kong (Project No. 17503219) for generous financial support.

Keywords

  • Annuitization choices
  • Annuity price
  • Mutual dependence
  • Survival probability heterogeneity
  • Uniqueness of equilibrium

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