Title: Mathematics for Economics
Instructors: Matteo Brachetta, Mauro Rosestolato, Maria Laura Torrente
Credits (CFU): 3 CFU
Lectures: 24 hours (8 hours for each module)
Homework: 42 hours
Period Taught: November 2025 – January 2026
Course Description and objectives
This course aims at providing basic tools of optimization methods, with a special view on stochastic control problems in Economics and Finance. The course is divided in three modules.
The first module (Maria Laura Torrente) aims to provide the student with the knowledge of advanced mathematical methods to successfully deal with economic models from a quantitative viewpoint. More specifically, the course will introduce the student to both the unconstrained and the constrained optimization of functions of several variables.
The second module (Mauro Rosestolato) aims to give the student a taste of optimal control theory in continuous time via dynamic programming. After some motivating examples, the general optimal control problem is introduced. Bellman's principle of optimality, the Hamilton-Jacobi-Bellman equation, and their combined use to find an optimal control strategy will be presented and applied to simple cases.
The third module (Matteo Brachetta) is devoted to stochastic optimization. After a quick review on stochastic calculus, the student will be taught how to properly formulate stochastic control problems, and how to solve them with the classical methods based on the Hamilton-Jacobi-Bellman equation. This module will also cover some applications in Economics and Finance
Prerequisites
It is expected that students have prior knowledge of calculus and optimization in one variable and basic notions of linear algebra. Basics of probability theory are warmly recommended.
Course Materials
Lecture notes will generally contain all the material students are expected to learn.
In turn, the lectures will often refer to and closely follow the relevant chapters in:
- Simon, C., Blume, L.: Mathematics for Economists (1994), Norton and Company.
- Peccati, L., D'Amico, M., Cigola, M. : Maths for Social Sciences (2018), Springer.
- Knut Sydsaeter, Peter Hammond, Atle Seierstad, Arne Strom, "Further mathematics for Economic Analysis" (2nd edition), Pearson.
- Bischi, G.I., Lamantia, F., Radi, D.: Lectures Notes on Dynamical Systems in Economics and Finance (2014), available online.
- Pham, H. Continuous-time Stochastic Control and Optimization with Financial Applications (2009), Springer.
Assessment
Students will be assessed in the final exam, which will consist of questions on the the theoretical and modeling features treated in the course as well as exercises.