The present paper considers a class of general equilibrium economies when

the primitive uncertainty model features uncertainty about continuous-time

volatility. This requires a set of mutually singular priors, which do not share

the same null sets. For this setting we introduce an appropriate commodity

space and the dual of linear and continuous price systems.

All agents in the economy are heterogeneous in their preference for uncer-

tainty. Each utility functional is of variational type. The existence of equi-

librium is approached by a generalized excess utility fixed point argument.

Such Arrow-Debreu allocations can be implemented into a Radner economy

with continuous-time trading. Effective completeness of the market spaces al-

ters to an endogenous property. Only mean unambiguous claims equivalently

satisfying the classical martingale representation property build the marketed

space.