We propose a stochastic control approach to the dynamic maximization ofrobust 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...

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...

As a main step in the numerical solution of control problems in continuous time,the controlled process is approximated by sequences of controlled Markov chains, thus discretising time and space. A new feature in this context is to allow for delay in the dynamics. The existence of an optimal...