This repository contains a series of quantitative projects focusing on stochastic modeling, risk analysis, and algorithmic backtesting.

• Concepts: Monte Carlo Methods, Law of Large Numbers, Central Limit Theorem.
• Outcome: Proved the Monty Hall paradox and established 95% confidence intervals for simulated win rates.

• Concepts: Log-Normal Distributions, Volatility Drag, Sequence of Returns Risk.
• Outcome: Modeled 30-year wealth projections with power metrics.

• Concepts: Time-Series Analysis, Trend Following, Risk-Adjusted Returns (Sharpe Ratio).
• Outcome: Developed a systematic SMA Crossover backtester using 26 years of historical S&P 500 data. Demonstrated capital preservation through Maximum Drawdown reduction during major market regimes (2008, 2022).