Ambiguity and the Language of Long Run Risk

This paper investigates a duality between ambiguity averse preferences and the valuation of long run risky assets or public projects. The variational ambiguity model represents preferences over ambiguous acts via a minimization problem, and is fundamentally nonprobabilistic. In contrast, long run risky assets are ranked via a large maturity limit of expected discounted returns. Despite their apparent differences, we show that each variational ambiguity preference is a long run risk preference, and (under natural conditions) vice versa. We explore three implications: a notion of long run stochastic dominance that resolves differences between stochastic processes considered identical by standard risk measures, a typology of stochastic processes that pinpoints when a non-probabilistic description of long run risk is required, and an evolutionary foundation for variational ambiguity preferences that offers a novel explanation for ambiguity aversion.