We study optimal buying and selling strategies in target zone models. Such models describe situations in which a currency exchange rate is kept above or below certain barriers due to central bank intervention. We first consider the problem a central bank is facing when defending a lower currency peg against a macroeconomic trend. The goal of the central bank is to minimize its inventory of foreign currency and to keep slippage low. The mathematical formulation of this problem leads to a two-point boundary value problem with infinite boundary conditions, which can be solved by a reduction to a theorem by Lasry and Lions (1989). Then we consider an optimal portfolio liquidation problem for an investor for whom prices are optimal at the lower currency peg and who creates temporary price impact. This problem will be formulated as the minimization of a cost-risk functional over strategies that only trade when the price process is located at the barrier. We solve the corresponding singular stochastic control problem by means of a scaling limit of critical branching particle systems, which is known as a catalytic superprocess. The talk is based on joint work with Eyal Neuman, Chengguo Weng, and Xiaole Xue.

BIO

Alexander Schied is professor at the University of Waterloo. His research is in probability theory and stochastic analysis with applications to mathematical finance and economics. Recent research topics include risk measurement and risk management, modeling and optimization in finance and economics, robustness and model uncertainty, and issues arising from market microstructure and price impact. Together with Hans Föllmer he co-authored the book Stochastic Finance: An Introduction in Discrete Time. He holds a doctoral degree in mathematics from the University of Bonn.