Course detail

Financial Mathematics

FSI-SFI-AAcad. year: 2025/2026

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

Mode of study

Not applicable.

Guarantor

RNDr. Pavel Popela, Ph.D.

Department

Institute of Mathematics (ÚM)

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.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Brandimarte, P.: Numerical Methods in Finance: A MATLAB-Based Introduction. 1st edition, Wiley - Interscience, 2001. (EN)
Dupačová,J. et al.: Stochastic Models for Economics and Finance, Kluwer, 2003. (EN)

Recommended reading

Brandimarte, P.: Numerical Methods in Finance: A MATLAB-Based Introduction. 1st edition, Wiley - Interscience, 2001. (EN)
Capinski, M., Zastawniak, T.: Mathematics for Finance: An Introduction to Financial Engineering. Springer Verlag, 2003. (EN)
Cipra T.: Financial and Insurance Formulas, Springer-Verlag, 2010. (EN)
Dupačová,J. et al.: Stochastic Models for Economics and Finance, Kluwer, 2003. (EN)

Classification of course in study plans

  • Programme N-AIM-A Master's 2 year of study, winter semester, compulsory
  • Programme N-MAI-A Master's 2 year of study, winter semester, compulsory
  • Programme N-MAI-P Master's 2 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

RNDr. Pavel Popela, Ph.D.

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 hod., compulsory

Teacher / Lecturer

RNDr. Pavel Popela, Ph.D.

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.