Mathematics & Probability
The mathematical building blocks that underpin every trading system and risk model.
7 lessons · 64 min total
1
Nash Equilibrium and No Arbitrage
Understand where edge exists, why most setups fail over time, and how competitive balance shapes modern markets.
8 min read
2
Variance & Standard Deviation
Measure the dispersion of returns to understand risk, compare strategies, and set realistic performance expectations.
9 min read
3
Skewness & Kurtosis
Go beyond mean and variance to examine the asymmetry and tail thickness of return distributions and why they matter for risk.
9 min read
4
Monte Carlo Simulations
Use randomized simulations to stress-test strategies, estimate drawdown distributions, and build confidence intervals around expected returns.
10 min read
5
Bayesian Thinking
Update your beliefs as new evidence arrives using Bayes theorem -- a framework for evolving your system without abandoning it.
9 min read
6
The Kelly Criterion
Apply the Kelly formula and its fractional variants to find the theoretically optimal bet size that maximizes geometric growth rate.
8 min read
7
Law of Large Numbers & Confidence Intervals
Build statistical confidence in your edge by understanding sample sizes, confidence intervals, and why 10 trades prove nothing.
11 min read