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Course detail

Financial Mathematics

Course unit code: FSI-SFI
Academic year: 2016/2017
Type of course unit: compulsory
Level of course unit: Master's (2nd cycle)
Year of study: 2
Semester: winter
Number of ECTS credits:
Learning outcomes of the course unit:
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.
Mode of delivery:
90 % face-to-face, 10 % distance learning
Prerequisites:
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.
Co-requisites:
Not applicable.
Recommended optional programme components:
Not applicable.
Course contents (annotation):
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.
Recommended or required reading:
Cipra, T. Finanční matematika v praxi, HZ 1993
Dupačová,J. et al.: Stochastic Models for Economics and Finance, Kluwer, 2003.
Planned learning activities and teaching methods:
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.
Assesment methods and criteria linked to learning outcomes:
Graded course unit credit is awarded on the basis of a written exam and the discussion in the group of participating students.
Language of instruction:
Czech
Work placements:
Not applicable.
Course curriculum:
Not applicable.
Aims:
The basic concepts and models of financial problems are accompanied by the theory and simple examples.
Specification of controlled education, way of implementation and compensation for absences:
Attendance of students is required and checked by students’ activity. Missed lessons are compensated by additional assignments.

Type of course unit:

Lecture: 26 hours, 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.
seminars in computer labs: 13 hours, 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.

The study programmes with the given course