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Intertemporal Asset Pricing under Knightian Uncertainty

Larry G. Epstein
Tan Wang

Abstract

In conformity with the Savage model of decision-making, modern asset pricing theory assumes that agents' beliefs about the likelihoods of future states of the world may be represented by a probability measure. As a result, no meaningful distinction is allowed between risk, where probabilities are available to guide choice, and uncertainty, where information is too imprecise to be summarized adequately by probabilities. In contrast, Knight and Keynes emphasized the distinction between risk and uncertainty and argued that uncertainty is more common in economic decision-making. Moreover, the Savage model is contradicted by evidence, such as the Ellsberg Paradox, that people prefer to act on known rather than unknown or vague probabilities. This paper provides a formal model of asset price determination in which Knightian uncertainty plays a role. Specifically, we extend the Lucas (1978) general equilibrium pure exchange economy by suitably generalizing the representation of beliefs along the lines suggested by Gilboa and Schmeidler. Two principal results are the proof of existence of equilibrium and the characterization of equilibrium prices by an "Euler inequality." A noteworthy feature of the model is that uncertainty may lead to equilibria that are indeterminate, that is, there may exist a continuum of equilibria for given fundamentals. That leaves the determination of a particular equilibrium price process to "animal spirits" and sizable volatility may result. Finally, it is argued that empirical investigation of our model is potentially fruitful.