The present paper considers a class of general equilibrium economics 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...

We reconsider the microeconomic foundations of financial economics under Knightian Uncertainty. In a general framework, we discuss the absence of arbitrage, its relation to economic viability, and the existence of suitable nonlinear pricing expectations. Classical financial markets under risk...

Under risk, Arrow-Debreu equilibria can be implemented as Radner equilibria by continuous trading of few long-lived securities. We show that this result generically fails if there is Knightian uncertainty in the volatility. Implementation is only possible if all discounted net trades of the...

We study the pricing of contracts in fixed income markets in the presence of volatility uncertainty. We consider an arbitrage-free bond market under volatility uncertainty. The uncertainty about the volatility is modeled by a G-Brownian motion, which drives the forward rate dynamics. The absence...

We show how to set up a forward rate model in the presence of volatility uncertainty by using the theory of G-Brownian motion. In order to formulate the model, we extend the G-framework to integration with respect to two integrators and prove a version of Fubini's theorem for stochastic...

It is shown how to construct an arbitrage-free short rate model under uncertainty about the drift and the volatility. The uncertainty is represented by a set of priors, which naturally leads to a G-Brownian motion. Within this framework, it is shown how to characterize the whole term structure...

This paper establishes, in the setting of Brownian information, a general equilibrium existence result under a stochastic differential formulation of intertemporal recursive utility. The present class of utility functionals is generated by a backward stochastic differential equation and...