Simulation of stochastic differential equations using the Monte Carlo method and Python

Navigating in the fog is difficult, but not impossible. Poland 2020. Photo by the author.

Introduction

This is the second part of the work that attempts to find a recipe towards financial independence — a stage where you no longer need to work to support yourself.

In the previous article, we tried to formulate the problem of personal finance through a system of ordinary differential equations (ODE), which we later solved numerically using python. Given a set of input parameters, our numerical model was able to determine your financial condition [Github].

In this article, we bring it to the next stage. We add randomness to the equation to account for life’s unpredictability. This time, we want to find out to what degree your financial success is really in your hands?

We will begin this journey by revisiting the math and add some random contributions. Then, we move into simulating some hypothetical scenarios using the so-called Monte Carlo method. Finally, we will use our augmented model to predict your chances with the help of the world’s historical data.

#data-science #mathematics #personal-development #finance #python