OVERVIEW

The aim of the course is to provide the student with the knowledge of advanced mathematical methods to successfully deal with economic models from a quantitative viewpoint.

AIMS AND CONTENT

LEARNING OUTCOMES

The course introduces the main mathematical tools for the analysis of continuous-time dynamic systems and intertemporal optimization problems. The first part reviews integration theory and ordinary differential equations: first-order separable and linear ODEs, equilibria and stability, second-order linear ODEs with constant coefficients, and first-order linear systems. The second part focuses on continuous-time optimal control through dynamic programming. Topics include the formulation of dynamic optimization problems, the Dynamic Programming Principle, the Hamilton-Jacobi-Bellman equation, the verification theorem, and applications to economics.

AIMS AND LEARNING OUTCOMES

At the end of the teaching unit, students will be able to handle, understand, and apply the mathematical tools learned. The expected learning outcomes are as follows.

• Knowledge and Understanding: Students must acquire adequate knowledge and effective understanding of the mathematical tools presented in the course.

• Ability to Apply Knowledge and Understanding: Students must be able to apply the acquired knowledge to understand and solve, from a mathematical perspective, relevant problems in the economic field.

• Independent Judgment: Students must be able to use the acquired knowledge both conceptually and operationally, with independent evaluation skills and ability in different applied contexts.

• Communication Skills: Students must acquire the technical language typical of the discipline to communicate clearly and unambiguously with both specialist and non-specialist audiences.

• Learning Skills: Students must develop adequate learning skills enabling them to continue using the assimilated mathematical tools, especially in future disciplines."

PREREQUISITES

The contents of the course of Mathematics for Economics and Data Sciences I.

TEACHING METHODS

• The teaching unit is delivered through lectures and exercises. Attendance is not compulsory.
• Students with disabilities, with SLD or with SEN are reminded that, to request exam accommodations, they must first upload their certification to the University website at servizionline.unige.it <https://servizionline.unige.it/>, in the “Students” section. The documentation will be checked by the University’s Services for the Inclusion of Students with Disabilities and with SLD. At the beginning of the course, students are advised to contact the lecturer to agree on exam arrangements which, while respecting the learning objectives of the course, take individual learning needs into account. To request compensatory tools or dispensatory measures, students with disabilities or SLD must fill in the dedicated Webform available athttps://unige.it/disabilita-dsa, at least 7 working days before the exam. Students with SEN may instead send their request by e-mail to the lecturer, copying the Department Representative, Prof. Elena Lagomarsino, at inclusione.economia@unige.it<mailto:inclusione.economia@unige.it>, and the Inclusion Office at   inclusione.studenti@info.unige.it <mailto:inclusione.studenti@info.unige.it>. Requests from students will be assessed by the lecturer and may be approved or rejected.

SYLLABUS/CONTENT

• Review of Integration Theory

• Ordinary Differential Equations (ODEs):

  • First-order separable ODEs

  • First-order linear ODEs

  • Equilibria and stability for autonomous first-order ODEs

  • Second-order linear ODEs with constant coefficients

  • First-order linear systems of ODEs

  • Stability for linear ODEs and systems

• Continuous time Optimal Control via Dynamic Programming:

  • Formulation of dynamic optimization problems

  • Dynamic Programming Principle

  • Hamilton-Jacobi-Bellman equation

  • Verification theorem

  • Applications to Economics

RECOMMENDED READING/BIBLIOGRAPHY

• Sydsaeter, K., Hammond, P., Seierstad, A., Strom, A.: Further Mathematics for Economic Analysis (2008), Pearson
• Simon, C., Blume, L.: Mathematics for Economists (1994), Norton and Company
• Peccati, L., D'Amico, M., Cigola, M. : Maths for Social Sciences (2018), Springer

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

Second semester, February 2027.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam will be written and will contain questions on the the theoretical and modeling features treated in the course as well as exercises.

ASSESSMENT METHODS

The exam will evaluate the understanding of the contents of the course with the goal of assessing the reached skill of applying the tools and the methods learned in an economic perspective

FURTHER INFORMATION

Other information will be provided during the course.