Optimal portfolio liquidation in target zone models and catalytic superprocesses

Eyal Neuman () and Alexander Schied ()
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Eyal Neuman: Hong Kong University of Science and Technology
Alexander Schied: University of Mannheim

Finance and Stochastics, 2016, vol. 20, issue 2, No 7, 495-509

Abstract: 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.

Keywords: Optimal portfolio liquidation; Market impact; Target zone models; Optimal stochastic control; Catalytic superprocess; 60J80; 60J85; 93E20; 60H20; 60H30; 91G80 (search for similar items in EconPapers)
JEL-codes: C02 C61 G11 G12 G18 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (10)

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DOI: 10.1007/s00780-015-0280-0

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