Dr. Stephan Sturm (ORFE, Princeton University)

Title: Portfolio optimization under convex incentive schemes: Duality theory and stochastic volatility

Abstract: We consider the utility maximization problem from the point of view of a portfolio manager paid by a convex incentive scheme. This problem departs from classical portfolio optimization theory since the implied utility function is no more concave which produces some interesting phenomena. Using duality theory, we are able top prove existence and uniqueness of the optimal wealth in general (incomplete) semimartingale markets as long as the unique optimizer of the dual problem has no atom with respect to the Lebesgue measure. In many cases, this fact is independent of the incentive scheme and depends only on the structure of the set of equivalent local martingale measures. As example we discuss stochastic volatility models and show that existence and uniqueness of an optimizer are guaranteed as long as the market price of risk satisfies a certain (Malliavin-)smoothness condition. This is joint work with Maxim Bichuch.