Course content

Stochastic Calculus, Control and Optimization with Applications in Finance is a PhD course offered by the Department of Industrial Economics and Technology Management within the scope of quantitative finance and operations research. Financial economics is a branch of economics that studies agent decisions involving money, time, and uncertainty. Most of the agents' decisions can be formalized as (stochastic) optimization problems. When considering continuous time models, agents’ decisions can be formalized as stochastic control problems.

This course provides students with some essential concepts in stochastic calculus and stochastic control, creating the basis for studying optimization models. Some of the topics in stochastic calculus are martingales, geometric Brownian motion, Itô lemma, the Feynman-Kac formula, and the Black-Scholes model. Regarding the optimization part, topics like stochastic control, optimal stopping, and optimal switching are covered. Analytical and numerical approaches may be discussed throughout the course. Finance and economics models will be presented and explored.

Learning outcome

After having completed the course, the candidate should:

- have competencies in stochastic calculus;

- be able to clearly distinguish between the different control problems discussed;

- formalize financial problems as stochastic optimization problems;

- know how to approach such problems (either numerically or analytically).

Learning methods and activities

Lectures. Participation in the seminars is expected, which includes attendance at all lectures, as well as contributions to the discussions.

Recommended previous knowledge

This course is designed for PhD candidates within the fields of operations research, finance, economics, statistics, and mathematics.

Required previous knowledge

Admission to a PhD programme within operations research, finance, statistics, and mathematics.

Course materials

Selected literature. Will be given at course start-up.