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An Optimal Stopping Problem of Detecting Entry Points for Trading Modeled by Geometric Brownian Motion

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Abstract

A “buy low, sell high” trading practice is modeled as an optimal stopping problem in this paper. Because its award function lacks sufficient smoothness, traditional free-boundary approach with solution in form of integral equations is not available. Therefore, we design a backward recursive algorithm computing the value function to determine the stopping boundary. Besides, a new PDE technique is developed to conclude the special cases with positive drift. Finally, groups of comparison tests are designed to investigate the model parameters setting as well as the feasibility and profitability of the trading strategy.

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Authors and Affiliations

  1. School of Finance and Economics, Jiangsu University, Zhenjiang, China

    Yue Liu, Jijian Zhang & Jingjing Yao

  2. College of Economics and Management, Nanjing Forestry University, Nanjing, China

    Aijun Yang

Authors
  1. Yue Liu
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  2. Aijun Yang
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  3. Jijian Zhang
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  4. Jingjing Yao
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Correspondence to Aijun Yang.

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This research is supported by Humanities and Social Science Foundation of Ministry of Education of China No. 18YJC910001, Jiangsu Natural Science Foundation No. BK20180852, China Postdoctoral Science Foundation No. 2017M621637, Natural Science Foundation of China Nos. 71673117 and 71701082, National Statistical Science Research Project of China No. 2017LY45, Startup Fundation of UJS No. 17JDG051, University Philosophy and Social Science Research Project of Jiangsu Province No. 2018SJA0130 and Jiangsu Qinglan Project (2017).

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Liu, Y., Yang, A., Zhang, J. et al. An Optimal Stopping Problem of Detecting Entry Points for Trading Modeled by Geometric Brownian Motion. Comput Econ 55, 827–843 (2020). https://doi.org/10.1007/s10614-019-09915-w

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