We consider optimal consumption and portfolio choice in the presence of Knightian uncertainty in continuous time. We embed the problem into the new framework of stochastic calculus for such settings, dealing in particular with the issue of non-equivalent multiple priors. We solve the problem...

A choice problem is risky (respectively ambiguous) if the decision maker is choosing between probability distributions (respectively sets of probability distributions) over utility relevant consequences. We provide an axiomatic foundation for and a representation of continuous linear preferences...

We analyze a static partial equilibrium model where the agents are not only heterogeneous in their beliefs about the return on risky assets but also in their attitude to it. While some agents in the economy are subjective utility maximizers others behave ambiguity averse in the sense of Knight...

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 a dynamic and infinite-dimensional model with Knightian uncertainty modeled by incomplete multiple prior preferences. In interior efficient allocations, agents share a common risk-adjusted prior and use the same subjective interest rate. Interior efficient allocations and equilibria...

In this paper we give an alternative characterization for time-consistent sets of measures in a discrete setting. For each measure p in a time-consistent set P we get a distinct set of predictable processes which in return describe the p uniquely. This implies we get a one-to-one correspondence...

We develop a theory of optimal stopping problems under ambiguity in continuous time. Using results from (backward) stochastic calculus, we characterize the value function as the smallest (nonlinear) supermartingale dominating the payoff process. For Markovian models, we derive an adjusted...