### Course: Financial Mathematics

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 Course title Financial Mathematics KSY/FPM Lecture + Lesson Bachelor not specified Winter 3 Czech Compulsory-optional Face-to-face Course does not contain work placement None
Lecturer(s)
• Tatek Benetti Karina, Ing. Ph.D.
Course content
Lectures (topics): Modules 0 - IV (1st - 7th lecture) are devoted to the basics of financial mathematics. Modules V. and VI. are devoted to the basics of actuarial mathematics. 0. Mathematical support: 1. Percentage, an overview of elementary functions, sequences, series, limits, averages. I. Overview of different types of interest and their practical use. 2. Simple interest, current and future capital value, decursive and anticipative interest. Equivalence interest rate. 3. Compound interest. Interest multiplier. Current and future value. Effective interest rate and interest intensity II. Application of different types of interest and discounting: 4. Application of simple anticipative interest, application of simple discounting, investment decision-making. III. Recurring payments and their use: 5. Saving: short-term, long-term, decursive and anticipative saving, a combination of short-term and long-term saving. 6. Pensions - temporary annuity: immediate decursive and anticipative annuity, immediate decursive and anticipative pension with more frequent pay than annual, perpetuity annuity, deferred annuity. IV. Amortisation and its practical use: 7. Paying off with equal instalments, paying off with the same loan, mortgage credit, APR. V. Life insurance: 8. Modelling mortality, mortality tables. 9. Basic kinds of life insurance and their valuation. 10. Life insurance premium calculation. VI. Non-life insurance: 11. Tariff groups and fundamental indicators in non-life insurance. 12. Non-life insurance premiums calculation. 13. Technical provisions and mathematical modelling in non-life insurance. Seminars: Solving practical exercises based in the lectures.

Learning activities and teaching methods
Monological explanation (lecture, presentation,briefing), Self-study (text study, reading, problematic tasks, practical tasks, experiments, research, written assignments), Demonstration, Project teaching
• Preparation for credit - 5 hours per semester
• Home preparation for classes - 24 hours per semester
• Preparation for exam - 5 hours per semester
• Class attendance - 56 hours per semester
Learning outcomes
TThe aim of the course is to introduce students to the basics of financial and actuarial mathematics. The issues of basic financial mathematics, mathematical methods, tools and applications in the financial sector are discussed in the section devoted to financial mathematics. The basics of actuarial mathematics, namely the concepts and principles of life and non-life insurance in the Czech Republic and the world are dealt with in the section devoted to actuarial mathematics.
Students obtain knowledge in given course in accordance with requirements and course programme.
Prerequisites
Knowledge of the subjects Mathematics.

Assessment methods and criteria
Written exam, Student's performance analysis

Conditions for credit: 85% of active participation in exercises; surrender two interim assignments. Conditions for exam: written exam, min. 65 % of the points.
Recommended literature
• Výsledky výzkumných projektů Analýza pojistného trhu I, II, III Katedry pojišťovnictví EF TUL, hrazené z NFVP, dostupné z WWW: &lt;http://www.nfvp.cz/projekty.html&gt; a také na webu EF TUL..
• Cipra, T. Finanční a pojistné vzorce.. Praha: Grada Publishing, 2006. ISBN 80-247-1633-X.
• Cipra, T. Pojistná matematika - teorie a praxe.. Praha : Ekopress, 2006. ISBN 80-86929-11-6.
• Macháček, O. Finanční a pojistná matematika, Praha. Prospektrum, 1995. ISBN 80-7175-035-2.
• McCutcheon, J. J., Scott, W. F. An Introduction to the Mathematics of Finace. Heinemann Professional Publishing Ltd., Oxford, 1989..
• Mužáková, K. ŽIVOTNÍ POJIŠTĚNÍ Vybraná řešení v MS Excel. Liberec, 2009. ISBN 9788073725099.
• PROMISLOW, D. S. Fundamentals of Actuarial Mathematics. John Wiley and Sons, 2011, 2nd Ed. 480 p. ISBN 978-80-47068-41-15..
• Radová, J. a kol. Finanční matematika pro každého příklady + CD ROM, Grada Publishing, Praha, 2007. ISBN 978-80-247-2364-8.
• Radová, J., Dvořák, P., Málek, J. Finanční matematika pro každého. 6. vyd. Grada Publishing, 2007. &, &. ISBN 978-80-247-2233-7.
• RICHARDSON, C., H. Financial Mathematics. New York: READ BOOKS, 2008. ISBN 978-14-437-2142-4.

 Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester