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• Introduction to SDEs
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The Mathematics of Allocating Risk Instead of Capital

This post explains risk parity through equal risk contribution, showing why capital weights can hide concentrated portfolio risk. We derive the core variance and risk contribution formulas, compare ERC with inverse-volatility weighting, and discuss covariance estimation, leverage, and regime risk.

• Risk Parity
• Equal Risk Contribution
• Portfolio Optimization
• Covariance Matrix
• Asset Allocation
• Risk Budgeting
• Hierarchical Risk Parity
• Quantitative Finance

Tuesday, June 16, 2026 Read

Introduction to Stochastic Differential Equations

This post introduces SDEs and the Euler-Maruyama method, demonstrating their application in finance and ESG modeling. Through F# simulations of stock prices and renewable energy adoption, we show how to implement and visualize SDE solutions, highlighting their importance for handling uncertainty.

• SDEs
• Euler-Maruyama
• F#
• Renewable Energy
• Financial Modeling

Saturday, August 9, 2025 Read

Simple Moving Average Crossover Strategy in F#

This post builds a simple moving average crossover strategy in F#, explaining short and long windows, crossover signals, thresholds, and the structure of a testable trading pipeline.

• Algorithmic Trading
• Quantitative Finance
• Time Series Analysis

Wednesday, April 2, 2025 Read

Attributing for Risk in Portfolio Management

This post explains portfolio risk attribution, showing how volatility and risk contribution formulas help identify which assets drive overall portfolio risk.

• Risk
• Portfolio Managemnt
• Volatility

Monday, December 2, 2024 Read