Optimal Portfolio Liquidation in Target Zone Models and Catalytic Superprocesses

Eyal Neuman
Hong Kong University of Science and Technology

We study optimal buying and selling strategies in target zone models. In these models the price is modeled by a diffusion process which is reflected at one or more barriers. Such models arise for example when a currency exchange rate is kept above a certain threshold due to central bank intervention. We consider trading strategies for a small trader for whom prices are optimal at the barrier and who creates temporary price impact. We formulate the minimization of a cost-risk functional of such strategies as a singular stochastic control problem. We solve this control problem by means of a scaling limit of critical branching particle systems, which is known as a catalytic superprocess. In this setting the catalyst is a set of points which is given by the barriers of the price process. This is joint work with Alexander Schied.

Back to Workshop II: The Mathematics of High Frequency Financial Markets: Limit Order Books, Frictions, Optimal Execution and Program Trading