  This paper formulates a model of utility for a continuous time framework that
captures the decision-maker's concern with ambiguity about both volatility and
drift. Corresponding extensions of some basic results in asset pricing theory
are presented. First, we derive arbitrage-free pricing rules based on hedging
arguments. Ambiguous volatility implies market incompleteness that rules out
perfect hedging. Consequently, hedging arguments determine prices only up to
intervals. However, sharper predictions can be obtained by assuming preference
maximization and equilibrium. Thus we apply the model of utility to a
representative agent endowment economy to study equilibrium asset returns. A
version of the C-CAPM is derived and the effects of ambiguous volatility are
described.
