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Optimal portfolio liquidation in target zone models and catalytic superprocesses

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Abstract

We study optimal buying and selling strategies in target zone models. In these models, the price is modelled 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 interventions. 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 is 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 given by the barriers of the price process. For the cases in which the unaffected price process is a reflected arithmetic or geometric Brownian motion with drift, we moreover give a detailed financial justification of our cost functional by means of an approximation with discrete-time models.

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Acknowledgement

The authors thank the Institute for Pure and Applied Mathematics at UCLA for the invitations to the workshop on The Mathematics of High Frequency Financial Markets, during which the research on this paper was completed. The authors furthermore thank Leo Speiser for helping with Fig. 1. A.S. gratefully acknowledges financial support by Deutsche Forschungsgemeinschaft through Research Grant SCHI/3-2.

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Authors and Affiliations

  1. Institute for Advanced Study, Hong Kong University of Science and Technology, Hong Kong, Hong Kong

    Eyal Neuman

  2. Department of Mathematics, University of Mannheim, 68131, Mannheim, Germany

    Alexander Schied

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  1. Eyal Neuman
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  2. Alexander Schied
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Correspondence to Eyal Neuman.

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Neuman, E., Schied, A. Optimal portfolio liquidation in target zone models and catalytic superprocesses. Finance Stoch 20, 495–509 (2016). https://doi.org/10.1007/s00780-015-0280-0

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  • DOI: https://doi.org/10.1007/s00780-015-0280-0

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