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 of the terminal wealth. The manager's own utility function is assumed to be smooth and strictly concave, however combining the utility function with the incentive scheme leads to an effective noncave utility function. As a consequence, the problem considered here does not fit into the classical portfolio optimization theory. We will show how one can use duality theory to prove existence and uniqueness of the optimal portfolio in general (incomplete) semimartingale markets as long as the unique optimizer of the dual problem has a continuous law. We will discuss explicit examples and will propose some open problems for further research. (Based on joint work with Maxim Bichuch).
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