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

TL;DR

This paper models a stock trading strategy based on support and resistance lines using optimal stopping theory, providing a mathematical framework for determining optimal buy and sell times under various market dynamics.

Contribution

It introduces a novel mathematical model linking support/resistance lines with optimal stopping, and derives explicit trading strategies for different market behaviors and risk preferences.

Findings

The value function is shown to be $C^1$ and solves a free boundary problem.

Optimal buy and sell times are characterized by linked free boundary problems.

Explicit strategies are computed for various dynamics and risk aversion levels.

Abstract

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 $C^1$ (with respect to the corresponding scale function) 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.