We formulate a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity or model uncertainty. The main novelty is in the range of model uncertainty that is accommodated. The probability measures entertained by the decision-maker are not assumed to be equivalent to a fixed reference measure and thus the model permits ambiguity about which scenarios are possible. Modeling ambiguity about volatility is a prime motivation and a major focus. A motivating application is the extension of asset pricing theory to incorporate ambiguity about volatility and possibility. The paper provides some initial steps in this direction by deriving equilibrium relations for asset returns in a representative agent framework, by deriving hedging bounds for asset prices, and by showing the pivotal role of `state prices' in both the equilibrium and no-arbitrage analyses .
This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both the drift and volatility of the driving process. At a technical level, the analysis requires a significant departure from existing continuous time modeling because it cannot be done within a probability space framework. This is because ambiguity about volatility leads invariably to a set of nonequivalent priors, that is, to priors that disagree about which scenarios are possible .
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or model uncertainty. The main novelty is in the range of model uncertainty that is accommodated. The probability measures entertained by the decision-maker are not assumed to be equivalent to a fixed reference measure and thus the model permits ambiguity about which scenarios are possible. Modeling ambiguity about volatility is a prime motivation and a major focus. A motivating application is the extension of asset pricing theory to incorporate
about both the drift and volatility of the driving process. At a technical level, the analysis requires a significant departure from existing continuous time modeling because it cannot be done within a probability space framework. This is because
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and possibility. The paper provides some initial steps in this direction by deriving equilibrium relations for asset returns in a representative agent framework, by deriving hedging bounds for asset prices, and by showing the pivotal role of `state prices' in both the equilibrium and no-arbitrage analyses
leads invariably to a set of nonequivalent priors, that is, to priors that disagree about which scenarios are possible