Before revision: 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.
After revision: We formulate 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 and possibility.