Survival with ambiguity

We analyze a market populated by expected utility maximizers and smooth ambiguity-averse consumers. We study conditions under which ambiguity-averse consumers survive and affect prices in the limit. If ambiguity vanishes with time or if the economy exhibits no aggregate risk, ambiguity-averse consumers survive, but have no long-run impact on prices. In both scenarios ambiguity-averse consumers are fully insured against ambiguity in equilibrium and thus behave as expected utility maximizers with correct beliefs. If ambiguity-averse consumers are not fully insured against ambiguity, their behavior mimics expected utility maximizers with wrong beliefs and a stochastic discount factor which might be consistently higher or lower than their actual discount factor. We use this insight to analyze a Markov economy with large persistent ambiguity. Consumers with decreasing absolute ambiguity aversion whose prudence with respect to ambiguity exceeds twice their absolute ambiguity aversion a.s. survive in the presence of expected utility maximizers with correct beliefs. If the economy further exhibits aggregate risk, they drive the expected utility maximizers out of the market and determine prices in the limit. In contrast, consumers with increasing or constant absolute ambiguity aversion only survive in the absence of aggregate risk and have no impact on limit prices.