Knightian Uncertainty in Financial Markets: An Assessment

Abstract

Following the Savage paradigm, the theory of portfolio choice and asset pricing under uncertainty assume that the agent's beliefs about future states of the world are represented by a unique additive probability measure, either objective or Bayesian prior. Given absence of arbitrage, agent optimality and market equilibrium, the price of any security is the discounted state-price weighted sum of its future payoffs. Each asset is valued by the expectation of its random payments with respect to the probability distribution over the state space. However, puzzling behavior such as price booms and crashes, excess volatility of asset prices, violation of call and put parity, bid and ask spreads and portfolio rigidities has been observed, in financial markets. All these phenomena can be explained by introducing transaction costs, asymmetric information, incomplete markets into standard financial market theory. In the last decade, following a reexamination process that has involved expected utility theory, several non-expected utility models have appeared in economic literature. The starting point is the distinction between risk, where the agent's beliefs are represented by a unique additive probability distribution, and Knightian uncertainty, where information is too vague and imprecise to be summarized by a unique additive probability measure. Since Knightian uncertainty is more common than risk in economic decision-making, researchers have introduced the agent's attitude towards ambiguity, proving that it plays a crucial role in asset price determination and portfolio choice. This provided an alternative explanation of financial market failures and enabled puzzles to be solved. In static and dynamic models, it was proved that Knightian uncertainty, summarized by a capacity or multiple priors, is a sufficient condition to induce phenomena such as price indeterminacy, price volatility, bid and ask spreads, portfolio inertia, violation of call and put parity and market breakdowns.