Heterogeneous beliefs among market participants can lead to questionable speculative trading that goes beyond any risk-sharing motives. We demonstrate that such unwarranted betting behavior in market equilibrium can be mitigated by introducing nonlinear pricing for ambiguous contracts, without...

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...

Cerreia-Vioglio, Ghirardato, Maccheroni, Marinacci and Siniscalchi (Economic Theory, 48:341-375, 2011) have recently proposed a very general axiomatisation of preferences in the presence of ambiguity, viz. Monotonic Bernoullian Archimedean (MBA) preference orderings. This paper investigates the...

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...

In this paper we study a two-player investment game with a first mover advantage in continuous time with stochastic payoffs, driven by a geometric Brownian motion. One of the players is assumed to be ambiguous with maxmin preferences over a strongly rectangular set of priors. We develop a...

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...

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...

The alpha-maxmin model is a prominent example of preferences under Knightian uncertainty as it allows to distinguish ambiguity and ambiguity attitude. These preferences are dynamically inconsistent for nontrivial versions of ». In this paper, we derive a recursive, dynamically consistent...

We develop a theory of optimal stopping problems under G-expectation framework. We first define a new kind of random times, called G-stopping times, which is suitable for this problem. For the discrete time case with finite horizon, the value function is defined backwardly and we show that it is...

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...