Engineering and applied research projects in stochastic modeling, machine learning, statistical analysis, and quantitative finance.
Stochastic differential equations course project | May 2026
Co-authors: Alejandro Yepiz and Arush Kannan
This project studies a practical modeling risk: a deterministic mean wind speed can underpredict expected wildfire rate of spread when wind enters a convex spread model. The work combines an Ornstein-Uhlenbeck wind process, Ito calculus, Monte Carlo simulation, and public NOAA observations from stations near the 2017 Thomas Fire.
| Evidence | Result |
|---|---|
| Nearest selected station | KCMA Camarillo Airport, 22.709 km from the CAL FIRE incident location |
| Empirical Jensen bias | 1.135 m/min |
| Second-order analytical correction | 1.107 m/min |
| Relative underprediction at mean observed wind | Approximately 11.5% |
The analytical correction was within approximately 2.5% of the observed bias at KCMA, and empirical bias was positive across all six nearby NOAA stations studied.
Methods: Stochastic differential equations, Ito's lemma, Jensen's inequality, Euler-Maruyama simulation, Monte Carlo validation, OU calibration, public-data engineering, uncertainty quantification
Read the project summary | Open the technical report
| Project | Focus | Evidence and deliverables |
|---|---|---|
| Reinforcement Learning with GRU and LSTM Networks | Time-series forecasting, backtesting, deep learning | Compared four model variants on SPY data and evaluated return, win rate, Sharpe ratio, and drawdown; includes a research poster. |
| Black-Scholes vs. Real Market Pricing | Statistical inference, option pricing | Compared theoretical and observed Target call-option prices using variance and mean tests; includes a notebook and report. |
| SPY Trading-Volume Control Charts | Statistical process control, event analysis | Used X-bar and R charts to evaluate assignable-cause variation around major market events; includes a notebook and report. |
| Bull Call Spread Analysis Tool | Options strategy modeling, Python | Computes breakeven, maximum profit and loss, probability estimates, leverage, and risk-reward measures. |
- Modeling: stochastic processes, uncertainty propagation, time-series forecasting, financial models
- Analysis: hypothesis testing, Monte Carlo simulation, statistical process control, backtesting
- Tools: Python, pandas, NumPy, Jupyter, yfinance, JMP
- Communication: technical reports, reproducible notebooks, research posters, reviewer-oriented summaries
Each project page states the research question, method, principal result, and available evidence. Claims are scoped to the data and assumptions used in the underlying work. Collaborative work is credited on its project page.