We consider a model for linear transient price impact for multiple assets that takes cross-asset impact into account. Our main goal is to single out properties that need to be imposed on the decay kernel so that the model admits well-behaved optimal trade execution strategies. We first show that...

We consider the infinite-horizon optimal portfolio liquidation problem for a von Neumann-Morgenstern investor in the liquidity model of Almgren (2003). Using a stochastic control approach, we characterize the value function and the optimal strategy as classical solutions of nonlinear parabolic...

We discuss whether Sanov's theorem can be extended to a topology that renders the mapping v --> |-> f dv continuous, for a given measurable function f. We show that this is possible if and only if f possesses all exponential moments with respect to the underlying law [mu]. AMS classification: 60F10

We introduce the notion of a convex measure of risk, an extension of the concept of a coherent risk measure defined in Artzner et aL (1999), and we prove a corresponding extension of the representation theorem in terms of probability measures on the underlying space of scenarios. As a case...

SFB 649 Discussion Paper 2005-025 Duality Theory for Optimal Investments under Model Uncertainty Alexander Schied * Ching-Tang Wu** * Technische Universität Berlin, Germany ** National University of Kaohsiung, Taiwan This research was supported by the...

SFB 649 Discussion Paper 2006-061 A Control Approach to Robust Utility Maximization with Logarithmic Utility and Time-Consistent Penalties Daniel Hernández–Hernández* Alexander Schied** * Centro de Investigación en Matemáticas, Guanajuato, Mexico **...