We provide a positive analysis of annuity puzzles using well-known models of ambiguity aversion, specifically second-order expected utility (SOEU) and multiplier preferences (MP). We show that, within a standard framework, such as Savage's expected utility theory, the annuity puzzle can emerge if the level of ambiguity aversion is sufficiently high in SOEU. In a richer setting, such as Anscombe and Aumann's expected utility framework, we also show that the annuity puzzle can emerge if the degree of model uncertainty becomes sufficiently high in MP. This latter finding provides a deeper understanding of how to account for multiple risks, which can encompass various aspects of decision environments, including health conditions, cognitive abilities, and life expectancies.