Infinite‐mean losses: insurance's “dread disease”

Purpose - The purpose of this paper is to consider the existence and significance of heavy‐tailed – and in particular, infinite‐mean – insurance losses. Design/methodology/approach - Three specific questions are addressed in turn. First, how do infinite‐mean insurance losses arise in the real world? Second, can infinite‐mean losses exist even in the presence of insurance policy limits (caps)? Third, why are infinite‐mean losses so infrequently discussed by practitioners and regulators? Findings - The paper first shows that heavy‐tailed – and in particular, infinite‐mean – insurance losses can be generated by simple modifications of gamma (exponential) random variables. It then finds that the property of infinite means cannot be prevented by the imposition of policy limits (caps). Finally, the paper argues that the statistical contagion and financial intractability of infinite‐mean losses generate a political fear among practitioners and regulators analogous to that associated with a “dread disease.” Originality/value - The paper explores an important insurance phenomenon – heavy‐tailed/infinite‐mean losses – that is insufficiently discussed.