Monte Carlo Method: A Simple Solution for Complex Problems

Overview

The Monte Carlo Method is a powerful computational algorithm that leverages repeated random sampling to obtain numerical results. It's particularly useful for solving deterministic problems that are too complex to tackle analytically. This repository demonstrates how the Monte Carlo Method can be used to estimate values such as π and compute integrals.

Why Monte Carlo?

• Versatility: Applicable in fields ranging from physics to finance.
• Simplicity: Easy to understand and implement.
• Robustness: Effective for complex problems where traditional methods fail.

Caveats

• Computationally Expensive: The Monte Carlo Method can be computationally expensive, especially for high-precision requirements or large-scale simulations.
• When Not to Use: Avoid using the Monte Carlo Method for simple, analytically solvable problems or where deterministic methods provide faster results.

Recommended Python Libraries

• NumPy: For efficient numerical computations.
• SciPy: For scientific and technical computing.
• Matplotlib: For plotting and visualizing the results.
• SymPy: For symbolic mathematics and algebra.

Applications

• Estimating π: A classic "Hello World" example. ✔️
• Calculating Integrals: Approximating complex integrals. ✔️
• Crypto Portfolio Optimization: Simulating asset allocations to optimize a portfolio. Yet to be done.

Getting Started

Explore the examples provided in this repository to see the Monte Carlo Method in action.