Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/195880 
Year of Publication: 
2018
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 6 [Issue:] 4 [Publisher:] MDPI [Place:] Basel [Year:] 2018 [Pages:] 1-15
Publisher: 
MDPI, Basel
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.
Subjects: 
mean reversion
HJB equation
quasi-variational inequalities
smooth-fit method
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
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