## Event Date:

## Event Location:

- Sobel Seminar Room

## Related Link:

- CFMAR Seminar Series

**Title**: Optimal Portfolio Liquidation in Target Zone Models

**Abstract**: 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 the optimal portfolio liquidation problem for an investor for whom prices are optimal at the barrier 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. In this setting the catalyst is a set of points which is given by the barriers of the price process.

Later, we consider the case where the investors create an additional permanent impact. The central bank, who wishes to keep the currency exchange rate above a certain barrier, therefore needs to buy its own currency. The permenent price impact, which is created by the transactions of both sides, turns the optimal trading problems of the trader and the central bank into coupled singular control problems, where the common singularity arise from a local time along a random curve. We solve the central bank's control problem by means of the Skorokhod map and derive the trader's optimal strategy by solving a sequence of approximated control problems. \

This is joint work with Alexander Schied.