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The Support and Resistance Line Method: An Analysis via Optimal Stopping

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  • Vicky Henderson
  • Saul Jacka
  • Ruiqi Liu

Abstract

We study a mathematical model capturing the support/resistance line method (a technique in technical analysis) where the underlying stock price transitions between two states of nature in a path-dependent manner. For optimal stopping problems with respect to a general class of reward functions and dynamics, using probabilistic methods, we show that the value function is $C^1$ and solves a general free boundary problem. Moreover, for a wide range of utilities, we prove that the best time to buy and sell the stock is obtained by solving free boundary problems corresponding to two linked optimal stopping problems. We use this to numerically compute optimal trading strategies for several types of dynamics and varying degrees of relative risk aversion. We then compare the strategies with the standard trading rule to investigate the viability of this form of technical analysis.

Suggested Citation

  • Vicky Henderson & Saul Jacka & Ruiqi Liu, 2021. "The Support and Resistance Line Method: An Analysis via Optimal Stopping," Papers 2103.02331, arXiv.org.
    • Handle: RePEc:arx:papers:2103.02331
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    References listed on IDEAS

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    3. Jun Maeda & Saul D. Jacka, 2017. "An Optimal Stopping Problem Modeling Technical Analysis," Papers 1707.05253, arXiv.org, revised Mar 2020.
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    6. Matthew Lorig & Zhou Zhou & Bin Zou, 2017. "A Mathematical Analysis of Technical Analysis," Papers 1710.09476, arXiv.org, revised Feb 2019.
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