Utility maximization in a general semimartingale model with nonlinear wealth dynamics

We use convex duality techniques to study the risk-averse utility maximization problem in a (non-markovian) multidimensional semimartingale market model. We assume the instantaneous expected return of the wealth dynamics is a non-linear function of the portfolio choices. This allows modeling the additional cash flow that results from a variety of market frictions, for instance, the funding cost arising from differential borrowing and lending rates, or the aggregate production inflow of a firm with constant return-to-scale Cobb-Douglas technology subject to exogenous shocks with jumps. In addition to providing a general result for additive utilities satisfying Inada conditions, we characterize explicitly optimal strategies for CRRA utilities.