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.
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