The question of general equilibrium in an incomplete financial market model is undertaken. Economic agents all have numeraire-invariant preferences, but different subjective beliefs and stochastic consumption clocks. The market contains a borrowing and lending account in zero net supply, as well as a stock in positive unit net supply providing certain dividend stream, exogenously specified. A characterization of existence and uniqueness of equilibrium is provided in terms of stochastic differential equations. The proposed framework naturally allows for equilibria where assets in positive net supply contain bubbles, even in the case of complete markets with unconstrained acting agents.