Expected Value (EV)
The long-run average outcome of a random variable.
Variance
Average squared deviation from the mean.
Standard Deviation
Square root of variance; measures volatility.
Random Variable
A variable whose value is determined by chance.
Law of Large Numbers
As sample size increases, sample average converges to the true mean.
Central Limit Theorem (CLT)
The sum/average of many independent random variables is approximately normal.
Normal Distribution
Bell-shaped distribution fully defined by mean and standard deviation.
Log-Normal Distribution
A distribution where the log of the variable is normal; used for stock prices.
Brownian Motion
A continuous random process with independent, normally distributed increments.
Geometric Brownian Motion
A stochastic process used to model stock prices; always positive.
Monte Carlo Simulation
Repeated random sampling to estimate expected outcomes.
Martingale
A process where the expected future value equals the current value.
Stochastic Process
A random process that evolves over time.
Value at Risk (VaR)
The maximum expected loss over a time period at a given confidence level.
Fat Tails
Higher probability of extreme outcomes than the normal distribution predicts.
Mean Reversion
The tendency of a variable to move back toward its average.
