In this paper we deal with the utility maximization problem with general utility functions including power utility with liability. We derive a new approach in which we reduce the resulting control problem to the study of a system of fully-coupled Forward–Backward Stochastic Differential...

<Para ID="Par1">We consider the terminal wealth utility maximization problem from the point of view of a portfolio manager who is paid by an incentive scheme, which is given as a convex function g of the terminal wealth. The manager’s own utility function U is assumed to be smooth and strictly concave;...</para>

We establish the existence and characterization of a primal and a dual facelift - discontinuity of the value function at the terminal time - for utility maximization in incomplete semimartingale-driven financial markets. Unlike in the lower- and upper-hedging problems, and somewhat unexpectedly,...

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...

For portfolio choice problems with proportional transaction costs, we discuss whether or not there exists a shadow price, i.e., a least favorable frictionless market extension leading to the same optimal strategy and utility. By means of an explicit counter-example, we show that shadow prices...