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Risks 2018, 6(4), 107; https://doi.org/10.3390/risks6040107

A Threshold Type Policy for Trading a Mean-Reverting Asset with Fixed Transaction Costs

1
Department of Mathematics, University of North Georgia, Oakwood, GA 30566, USA
2
Department of Mathematics, University of Georgia; Athens, GA 30602, USA
*
Author to whom correspondence should be addressed.
Received: 11 August 2018 / Revised: 16 September 2018 / Accepted: 22 September 2018 / Published: 29 September 2018
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Abstract

A mean-reverting model is often used to capture asset price movements fluctuating around its equilibrium. A common strategy trading such mean-reverting asset is to buy low and sell high. However, determining these key levels in practice is extremely challenging. In this paper, we study the optimal trading of such mean-reverting asset with a fixed transaction (commission and slippage) cost. In particular, we focus on a threshold type policy and develop a method that is easy to implement in practice. We formulate the optimal trading problem in terms of a sequence of optimal stopping times. We follow a dynamic programming approach and obtain the value functions by solving the associated HJB equations. The optimal threshold levels can be found by solving a set of quasi-algebraic equations. In addition, a verification theorem is provided together with sufficient conditions. Finally, a numerical example is given to illustrate our results. We note that a complete treatment of this problem was done recently by Leung and associates. Nevertheless, our work was done independently and focuses more on developing necessary optimality conditions. View Full-Text
Keywords: mean reversion; HJB equation; quasi-variational inequalities; smooth-fit method mean reversion; HJB equation; quasi-variational inequalities; smooth-fit method
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Luu, P.; Tie, J.; Zhang, Q. A Threshold Type Policy for Trading a Mean-Reverting Asset with Fixed Transaction Costs. Risks 2018, 6, 107.

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