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

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