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<p>We study a mathematical model motivated by the support/resistance line method in technical analysis, where the underlying stock price transitions between three 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 <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>1</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$C^{1}$</EquationSource> </InlineEquation> and solves a general free boundary problem. Moreover, for a range of utilities, we prove that the best times to buy and sell the stock are obtained by solving free boundary problems corresponding to two linked optimal stopping problems. We use this to compute optimal trading strategies for several types of dynamics and varying degrees of relative risk aversion.</p>

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The support and resistance line method: an analysis via optimal stopping

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月2日

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  • Vicky Henderson,
  • Saul Jacka,
  • Ruiqi Liu,
  • Jun Maeda

摘要

We study a mathematical model motivated by the support/resistance line method in technical analysis, where the underlying stock price transitions between three 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 $C^{1}$ and solves a general free boundary problem. Moreover, for a range of utilities, we prove that the best times to buy and sell the stock are obtained by solving free boundary problems corresponding to two linked optimal stopping problems. We use this to compute optimal trading strategies for several types of dynamics and varying degrees of relative risk aversion.