Technical University of Liberec
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for academic year 2025/2026
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Course: Financial Mathematics

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Course title Financial Mathematics
Course code KSY/FPM-E
Organizational form of instruction Lecture
Level of course Bachelor
Year of study not specified
Semester Winter and summer
Number of ECTS credits 6
Language of instruction English, English
Status of course unspecified
Form of instruction Face-to-face
Work placements Course does not contain work placement
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • Tatek Benetti Karina, Ing. Ph.D.
Course content
Lectures: Modules 0th to IVth (Lectures 1st to 7th) is devoted to the fundamentals of financial mathematics. Modules Vth and VIth are devoted to the fundamentals of actuarial mathematics. 0th Mathematical Support: 1st Percentage, an overview of elementary functions, sequences, series, limits, averages. Ist Overview of different types of interest and their practical use: 2nd Simple interest, present and future value of capital, interest. Equivalence interest rates. 3rd Compound interest. Current and future value. Effective interest rate and interest intensity. IInd Application of different types of interest and discounting: 4th Application of simple interest, discounting a simple application (bills and treasury bills), the investment decision-making. IIIrd Certain recurring payments and their use: 5th Savings: short savings and long-term savings, a combination of short and long-term savings. 6th Pensions - Retirement temporary: immediate annuity, immediate pension, pension eternal deferred pension. IVth Amortization and its practical use: 7th Amortization of debt in equal parts, bonded same amortization, mortgage loan, APR. Vth Life insurance: 8th Modelling mortality, mortality tables. 9th The basic types of life insurance and their valuation. 10th Calculation of premiums in life insurance. VIth Non-life insurance: 11th Tariff groups and basic indicators in non-life insurance. 12th Calculation of premiums in non-life insurance. 13th Technical reserves and mathematical modeling in general insurance. 14th Reserve Exercise: Exercise a follow-up to its individual modules, except module zero, one exercise works as a reserve. Selected examples will also be solved by using computers (PC) - Excel.

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
The aim of the course is to acquaint students with the basics of financial and actuarial mathematics. The section that deals with the basics of financial mathematics is the aim of this section to familiarize students with basic questions of financial mathematics, mathematical concepts, mathematical methods used in modern finance and financial instruments used in the field. Also also explain and derive the main mathematical methods and show specific application of these procedures in the financial - particularly banking practice. The section that deals with the basics of actuarial mathematics is the aim of this section to familiarize students with the basic concepts and principles of construction used in the life and non-life insurance in foreign and in the Czech Republic and thus gain a theoretical foundation and also an overview of the specific forms used by insurance comparison in terms of mathematical.
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
  • Materiály vzniklé na základě projektu FRVŠ č. 207/2009. Modulárně koncipovaný text teoretické části (7 modulů), 110 s. PowerPointové prezentace odpovídající modulárnímu konceptu (233 slaidů) a také sbírka příkladů (42 stran). .
  • On-line katalogy knihoven. .
  • Výsledky výzkumných projektů Analýza pojistného trhu I, II, III Katedry pojišťovnictví EF TUL, hrazené z NFVP, dostupné z WWW: <http://www.nfvp.cz/projekty.html> a také na webu EF TUL.. .
  • 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.
  • CIPRA, Tomáš. Finanční a pojistné vzorce. Finanční trhy a instituce. , 2006.
  • CIPRA, Tomáš. Finanční ekonometrie. 2., upravené vydání. Praha, 2013.
  • CIPRA, Tomáš. Matematika cenných papírů. Praha, 2013.
  • CIPRA, Tomáš. Pojistná matematika - teorie a praxe. Praha, 2006.
  • Macháček, O. Finanční a pojistná matematika, Praha. Prospektrum, 1995. ISBN 80-7175-035-2.
  • MACHÁČEK, Otakar. Finanční a pojistná matematika: úrok a úročení, modely opakovaných plateb, burzovní operace při složeném úročení, pojistné operace. 2. vyd. dopl. Praha, 2001.
  • 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.
  • MUŽÁKOVÁ, K. ŽIVOTNÍ POJIŠTĚNÍ Vybraná řešení v MS Excel. Liberec. 2009.
  • OLIVIERI, Annamaria a PITACCO, Ermanno. Introduction to insurance mathematics: technical and financial features of risk transfers. Berlin, 2011.
  • 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.
  • RADOVÁ, Jarmila; DVOŘÁK, Petr a MÁLEK, Jiří. Finanční matematika pro každého. 8. rozšířené vydání. Praha, 2013.
  • RICHARDSON, C., H. Financial Mathematics. New York: READ BOOKS, 2008. ISBN 978-14-437-2142-4.
  • ŠOBA, Oldřich a ŠIRŮČEK, Martin. Finanční matematika v praxi. 2., aktualizované a rozšířené vydání. Praha, 2017.
  • WÜTHRICH, Mario Valentin a MERZ, Michael. Financial modeling, actuarial valuation and solvency in insurance. Springer finance. Berlin, 2013.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Technical University of Liberec, date of update: 22.09.2025 23:50. Data created for academic year 2025/2026