An optimal mean-reversion trading rule under a Markov chain model

Jingzhi  Tie; Qing  Zhang

doi:10.3934/mcrf.2016012

Article Contents

2016, Volume 6, Issue 3: 467-488. Doi: 10.3934/mcrf.2016012

This issue Previous Article Characterizations of integral input-to-state stability for bilinear systems in infinite dimensions Next Article A semidiscrete Galerkin scheme for backward stochastic parabolic differential equations

An optimal mean-reversion trading rule under a Markov chain model

Jingzhi Tie^1, and
Qing Zhang^1,

1.
Department of Mathematics, University of Georgia, Athens, GA 30602

Received: January 31, 2015

Revised: June 30, 2015

Published: August 2016

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Abstract

This paper is concerned with a mean-reversion trading rule. In contrast to most market models treated in the literature, the underlying market is solely determined by a two-state Markov chain. The major advantage of such Markov chain model is its striking simplicity and yet its capability of capturing various market movements. The purpose of this paper is to study an optimal trading rule under such a model. The objective of the problem under consideration is to find a sequence stopping (buying and selling) times so as to maximize an expected return. Under some suitable conditions, explicit solutions to the associated HJ equations (variational inequalities) are obtained. The optimal stopping times are given in terms of a set of threshold levels. A verification theorem is provided to justify their optimality. Finally, a numerical example is provided to illustrate the results.

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Mathematics Subject Classification: Primary: 93E20, 91G80; Secondary: 49L20.

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