Ambiguity, also called Knightian or model uncertainty, is a key feature in financial modeling. A recent paper by Maccheroni et al. (2004) characterizes investor preferences under aversion against both risk and ambiguity. Their result shows that these preferences can be numerically represented in...

Robust utility functionals arise as numerical representations of investor preferences, when the investor is uncertain about the underlying probabilistic model and averse against both risk and model uncertainty. In this paper, we study the the duality theory for the problem of maximizing the...

We give an explicit PDE characterization for the solution of a robust utility maximization problem in an incomplete market model, whose volatility, interest rate process, and long-term trend are driven by an external stochastic factor process. The robust utility functional is defined in terms of...

We anlyze the stochastic control approach to the dynamic maximization of the robust utility of consumption and investment. The robust utility functionals are defined in terms of logarithmic utility and a dynamically consisten convex risk measure. The underlying market is modeled by a diffusion...

We give an explicit PDE characterization for the solution of the problem of maximizing the utility of both terminal wealth and intertemporal consumption under model uncertainty. The underlying market model consists of a risky asset, whose volatility and long-term trend are driven by an external...

We propose a stochastic control approach to the dynamic maximization of robust utility functionals that are defined in terms of logarithmic utility and a dynamically consistent convex risk measure. The underlying market is modeled by a diffusion process whose coefficients are driven by an...