Stochastic Processes for Finance and Economics

Introduction

Stochastic processes play a fundamental role in modeling uncertain phenomena in business and economics. In an era where understanding risk is paramount, these mathematical models allow us to quantify and navigate complex, seemingly random market parameters. Today, stochastic methods serve as the backbone for critical financial activities, ranging from the valuation of assets and pricing of insurance products, to interest rate forecasting and optimization under uncertainty.

The main objectives of this course are to provide a solid basis for the mathematical models used to describe financial uncertainty. Students will be introduced to the foundations of probability theory and stochastic processes. To support this theoretical learning, the course will utilize Python for simple simulations. This is not intended to build advanced programming skills, but rather to help students visualize the behavior of stochastic processes and gain intuition through practical examples.

Course content

1. Introduction to probability theory;
2. Discrete and continuous random variables;
3. Jointly distributed and independent random variables;
4. Discrete- and continuous-time Markov chains;
5. Discrete random walks;
6. Brownian motion (continuous random walk);
7. Martingales;
8. The Black&Scholes model and the Merton model in finance and economics:
9. Simulations via Monte Carlo methods.

Disclaimer

This is an excerpt from the complete course description for the course. If you are an active student at BI, you can find the complete course descriptions with information on eg. learning goals, learning process, curriculum and exam at portal.bi.no. We reserve the right to make changes to this description.