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 economies in which agents face Knightian uncertainty about state prices. Knightian uncertainty leads naturally to nonlinear expectations. We introduce a corresponding equilibrium concept with sublinear prices and prove that equilibria exist under weak conditions. In general, such...

We study economies in which agents face Knightian uncertainty about state prices. Knightian uncertainty leads naturally to nonlinear expectations. We introduce a corresponding equilibrium concept with sublinear prices and prove that equilibria exist under weak conditions. In general, such...

We consider fundamental questions of arbitrage pricing arising when the uncertainty model incorporates volatility uncertainty. With a standard probabilistic model, essential equivalence between the absence of arbitrage and the existence of an equivalent martingale measure is a folk theorem, see...

We establish a class of fully nonlinear conditional expectations. Similarly to the usage of linear expectations when a probabilistic description of uncertainty is present, we observe analogue quantitative and qualitative properties. The type of nonlinearity captures the agents sentiments of...

Ambiguity can be used as a strategic device in some situations. To demonstrate this, we propose and study a framework for normal form games where players can use Knightian uncertainty strategically. In such Ellsberg games, players may use Ellsberg urns in addition to the standard objective mixed...