Course detail
Financial Mathematics
FSI-SFI-A Acad. year: 2025/2026 Winter semester
The course presents basic financial models. It focuses on main concepts and computational methods. Several lectures are especially developed to make students familiar with optimization models.
Language of instruction
English
Number of ECTS credits
4
Supervisor
Department
Entry knowledge
The knowledge of Calculus and Linear Algebra together with probabilistic and statistical methods (including time series) as well as optimisation techniques within the framework of SOP and SO2 courses is required.
Rules for evaluation and completion of the course
Graded course unit credit is awarded on the basis of a written exam and the discussion in the group of participating students.
Attendance of students is required and checked by students’ activity. Missed lessons are compensated by additional assignments.
Aims
The basic concepts and models of financial problems are accompanied by the theory and simple examples.
The course is designed for students of mathematical engineering and is useful for students of applied sciences. The fundamental knowledge of financial models is presented.
The study programmes with the given course
Programme N-MAI-P: Mathematical Engineering, Master's, compulsory
Programme N-MAI-A: Mathematical Engineering, Master's, compulsory
Programme N-AIM-A: Applied and Interdisciplinary Mathematics, Master's, compulsory
Type of course unit
Lecture
26 hours, optionally
Syllabus
1. Basic concepts, money, capital and securities.
2. Simple and compound interest rate, discounting.
3. Investments, cash flows and its measures, time value of money.
4. Assets and liabilities, insurance.
5. Bonds, options, futures, and forwards.
6. Exchange rates, inflation, indices.
7. Portfolio optimization – classical model.
8. Postoptimization, risk, funds.
9. Twostage models in finance.
10. Multistage models in finance.
11. Scenarios in financial mathematics.
12. Modelling principles, identification of dynamic data.
13. Discussion on advanced stochastic models.
Computer-assisted exercise
13 hours, compulsory
Syllabus
Selected examples and exercises illustrating:
1. Basic concepts, money, capital and securities.
2. Simple and compound interest rate, discounting.
3. Investments, cash flows and its measures, time value of money.
4. Assets and liabilities, insurance.
5. Bonds, options, futures, and forwards.
6. Exchange rates, inflation, indices.
7. Portfolio optimization – classical model.
8. Postoptimization, risk, funds.
9. Twostage models in finance.
10. Multistage models in finance.
11. Scenarios in financial mathematics.
12. Modelling principles, identification of dynamic data.
13. Discussion on advanced stochastic models.
Course participance is obligatory.