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...

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 study continuous-time consumption and portfolio choice in the presence of Knightian uncertainty about interest rates. We develop the stochastic model that involves singular priors and analyze optimal behavior. When there is sufficiently large uncertainty about interest rates, the agent...

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...

Stock market variance-return or price relations are sometimes negative and sometimes positive. We explain these puzzling findings using a model with two ("bad" and "good") variances. In the model, conditional equity premium depends positively on bad variance and negatively on good variance....

In the presence of ambiguity on the driving force of market randomness, we consider the dynamic portfolio choice without any predetermined investment horizon. The investment criteria is formulated as a robust forward performance process, reflecting an investor's dynamic preference. We show that...

The objective of this article is to derive a general martingale characterization of G-Brownian motion, which generalizes the results obtained in Xu [17]. For this end, we first study some extensions of stochastic calculus with respect to G-martingales under the sublinear expectation spaces

We study the dynamic indifference pricing with ambiguity preferences. For this, we introduce the dynamic expected utility with ambiguity via the nonlinear expectation--G-expectation, introduced by Peng (2007). We also study the risk aversion and certainty equivalent for the agents with...

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...