Trading a mean-reverting asset: Buy low and sell high |
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Authors: | Hanqin Zhang [Author Vitae] |
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Affiliation: | a Academy of Mathematics and Systems Science, Academia Sinica, Beijing, 100080, China b Department of Mathematics, University of Georgia, Athens, GA 30602, United States |
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Abstract: | This paper is concerned with an optimal trading (buy and sell) rule. The underlying asset price is governed by a mean-reverting model. The objective is to buy and sell the asset so as to maximize the overall return. Slippage cost is imposed on each transaction. The associated HJB equations (quasi-variational inequalities) are used to characterize the value functions. It is shown that the solution to the original optimal stopping problem can be obtained by solving two quasi-algebraic equations. Sufficient conditions are given in the form of a verification theorem. A numerical example is reported to demonstrate the results. |
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Keywords: | Optimal stopping Quasi-variational inequalities Mean-reverting process |
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