Optimal liquidation in a finite time regime switching model with permanent and temporary pricing impact

Baojun Bian; Nan  Wu; Harry  Zheng

doi:10.3934/dcdsb.2016002

Article Contents

2016, Volume 21, Issue 5: 1401-1420. Doi: 10.3934/dcdsb.2016002

This issue Previous Article Positive solutions to elliptic equations in unbounded cylinder Next Article Free boundary problem of Barenblatt equation in stochastic control

Optimal liquidation in a finite time regime switching model with permanent and temporary pricing impact

1.
Department of mathematics, Tongji University, Shanghai 200092
2.
Department of Mathematics, Imperial College, London SW7 2BZ
3.
Department of Mathematics, Imperial College, London SW7 2AZ

Received: October 2013

Revised: March 2014

Published: July 2016

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Abstract

In this paper we discuss the optimal liquidation over a finite time horizon until the exit time. The drift and diffusion terms of the asset price are general functions depending on all variables including control and market regime. There is also a local nonlinear transaction cost associated to the liquidation. The model deals with both the permanent impact and the temporary impact in a regime switching framework. The problem can be solved with the dynamic programming principle. The optimal value function is the unique continuous viscosity solution to the HJB equation and can be computed with the finite difference method.

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Mathematics Subject Classification: Primary: 93E20; Secondary: 35D40.

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