We consider fundamental questions of arbitrage pricing arising when the uncertainty model incorporates volatility uncertainty. The resulting ambiguity motivates a new principle of preference-free valuation.

By establishing a microeconomic foundation of sublinear price systems, the principle of ambiguity-neutral valuation imposes the novel concept of equivalent symmetric martingale measures. Such measures exist when the

asset price with uncertain volatility is driven by Peng's G-Brownian motion.