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 language | English |
|---|---|
| Pages (from-to) | 146-156 |
| Number of pages | 11 |
| Journal | Insurance: Mathematics and Economics |
| Volume | 119 |
| Early online date | 30 Aug 2024 |
| DOIs | |
| Publication status | Published - 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