Entropic Risk Constraints for Utility Maximization

We consider the optimal selection of portfolios for utility maximizing investors under joint budget and risk constraints. The risk is measured in terms of entropic risk which is a convex risk measure. Stock returns satisfy a stochastic differential equation where we assume partial information on the drift. Under general conditions on the corresponding drift process we provide the optimal trading strategy using Malliavin calculus. We give numerical results for power utility and a model where the drift is a Markov process with finitely many states.