Probability Theory, Event Spaces and Fractals for Trading Analysis
Summary
This introductory article presents probability theory as a way to replace intuitive market judgments with measurable events and risks. It defines outcomes, event spaces, overlapping and non-overlapping events, and explains how event probabilities relate to the full set of possible outcomes. It also introduces probability density for outcomes described by continuous variables, using a two-dimensional target example to illustrate the idea.
The discussion connects these foundations to trading concepts such as expected value and risk, then turns to probability trees, Bernoulli trials and fractals. The author describes constructing a fractal from repeated two-state steps and says the approach was explored with a programming environment. The article is conceptual groundwork for a proposed later treatment of market processes as fractal-probability chains; it does not provide a tested trading strategy, market data results or evidence that the construction forecasts prices. Its claims are therefore mathematical and educational rather than empirical guidance on returns.
Key ideas
- Probability theory represents market questions through defined events and their possible outcomes.
- Probabilities across a collectively exhaustive set of non-overlapping events sum to one.
- Continuous outcome spaces can be described with probability density functions and integrals.
- Expected value and risk provide quantitative ways to compare trading systems.
- The article introduces Bernoulli trials and fractal construction but leaves market forecasting applications for later work.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.