Reducing Multi-Outcome Trading Strategies to a Two-State Model

Summary

This research article proposes approximating a sequential strategy with many possible trade outcomes as a two-state process with equal-sized up and down steps. The reduced model is described by the probability of an up step and the average formation times for up and down steps. The author matches long-run expected balance movement and elapsed time between the source strategy and the simplified process, then adds requirements that the models have the same probabilities and average times for reaching the bounds of a corridor.

The method is intended to make formulas developed for simple fractal or random-walk models applicable to more complex trade records. The article discusses simulation and parameter adjustment as ways to assess the transformation, and frames the work as a foundation for later trading-system development. It does not establish that the approximation preserves all relevant properties or demonstrate predictive or trading performance. The equations are presented as a research framework, and the conclusion acknowledges that implementation details and further refinement remain.

Key ideas

• A complex sequence of non-overlapping trades can be represented approximately as equal-sized up and down steps.
• The reduced process uses an up-step probability and separate average durations for upward and downward steps.
• The proposed matching criteria include long-run balance displacement, elapsed time, and corridor-boundary crossing behavior.
• Step size is a free choice in the framework, while other parameters are intended to be solved from matching equations.
• Simulation and adjustment are proposed, but the article does not establish that the reduction preserves strategy performance.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.