Course detail
Financial and Insurance Mathematics
FP-VfpmPAcad. year: 2017/2018
This course is a cross-section of modern methods and principals of financial and selected insurance calculations as they are applied in financial and insurance practice: types of interest rates, savings, systems of financial flows, investment rules, income, shares, bonds, debt amortization, financial risk, portfolio theory, basic insurance principles.
Language of instruction
Czech
Number of ECTS credits
6
Mode of study
Not applicable.
Guarantor
Department
Learning outcomes of the course unit
After completing the course, students will be able to understand the principles and function of the financial decision-making and to use acquired knowledge and skills for modeling of financial and insurance phenomena and solving of basic problems in these areas by conventional means of engineering mathematics.
Prerequisites
Basic courses university mathematics: percentages, adjustment of expressions, solving equations, inequations, and their systems, functions (basic terms, properties and graphs of elementary functions), sequences and series (especially arithmetic and geometric), averages. The basic use of mathematical software for computations, visualizations, simulations and modeling of financial phenomena. Orientation in selected categories in economic environment.
Co-requisites
Not applicable.
Planned learning activities and teaching methods
The course has two forms
- lectures that explain basic principles, problems and methodology of the discipline and there are solved typical examples and tasks,
- exercises that promote practical using theoretical knowledge from the lectures.
- lectures that explain basic principles, problems and methodology of the discipline and there are solved typical examples and tasks,
- exercises that promote practical using theoretical knowledge from the lectures.
Assesment methods and criteria linked to learning outcomes
Conditions for awarding the course-unit credit:
1. Active attendance at exercises which is obligatory, monitored, and assessed by teacher. The student is obliged to excuse his absence.
2. Continuous processing assigned tasks, and semester project.
3. Successful completion of a credit test (evaluation A to E).
Achievement of the conditions (1, 2, 3, above), resp. determination of corrective actions individually are fully in teacher's competence. The course-unit credit is a necessary prerequisite for the exam execution.
Conditions for exam:
The course-unit credit is a necessary prerequisite for the exam execution. Exam demonstrates knowledge of taught topics and its practical application. Form of examination is combined: a written part (60 minutes), and a short oral part. The core of exam is a written part. Oral part follows a written part and it is used to more specification of a final classification. To the exam are admitted only students who are logged into the BUT system. Classification methods depend on the BUT Rules for Studies and Examinations using the ECTS grading scale.
1. Active attendance at exercises which is obligatory, monitored, and assessed by teacher. The student is obliged to excuse his absence.
2. Continuous processing assigned tasks, and semester project.
3. Successful completion of a credit test (evaluation A to E).
Achievement of the conditions (1, 2, 3, above), resp. determination of corrective actions individually are fully in teacher's competence. The course-unit credit is a necessary prerequisite for the exam execution.
Conditions for exam:
The course-unit credit is a necessary prerequisite for the exam execution. Exam demonstrates knowledge of taught topics and its practical application. Form of examination is combined: a written part (60 minutes), and a short oral part. The core of exam is a written part. Oral part follows a written part and it is used to more specification of a final classification. To the exam are admitted only students who are logged into the BUT system. Classification methods depend on the BUT Rules for Studies and Examinations using the ECTS grading scale.
Course curriculum
Fundamentals of mathematical methods aimed to discipline - brief summary
Interest
Savings
Time value of money; Investment decision-making
Pensions
Loans; Installment plan
Bond
Shares
Portfolio theory
Future contracts; Speculation in securities; Currency rates
Insurance
Applications - practice
Interest
Savings
Time value of money; Investment decision-making
Pensions
Loans; Installment plan
Bond
Shares
Portfolio theory
Future contracts; Speculation in securities; Currency rates
Insurance
Applications - practice
Work placements
Not applicable.
Aims
The aim of the course is to acquaint students with the basic concepts and relations in the field of modern finance in the application of mathematical methods, applications in the real examples and other practical knowledge.
Specification of controlled education, way of implementation and compensation for absences
Attendance at lectures is not compulsory, but is recommended.
Attendance at exercises is compulsory and regularly monitored. Student must to excuse his absence. The independent processing of assigned tasks in excercises are checked. In the case of non-fulfilment given conditions in excercises the teacher can set additional condition.
Attendance at exercises is compulsory and regularly monitored. Student must to excuse his absence. The independent processing of assigned tasks in excercises are checked. In the case of non-fulfilment given conditions in excercises the teacher can set additional condition.
Recommended optional programme components
Not applicable.
Prerequisites and corequisites
Not applicable.
Basic literature
CIPRA, T.: Praktický průvodce finanční a pojistnou matematikou. Vyd. III. Praha: Ekopress. 308 s. 2015. ISBN: 978-80-87865-18-7. (CS)
KARATSAZ., I. and SHREVE, S.E. Methods of Mathematical Finance. 2. vydání. Springer. 1999. ISBN-13: 978-0387948393. (EN)
RADOVÁ, J., DVOŘÁK, P. and MÁLEK, J.. Finanční matematika pro každého. 8. rozšířené vydání. Praha: Grada Publishing, a.s. 304 s. 2013. ISBN:078-80-247-4831-3. (CS)
KARATSAZ., I. and SHREVE, S.E. Methods of Mathematical Finance. 2. vydání. Springer. 1999. ISBN-13: 978-0387948393. (EN)
RADOVÁ, J., DVOŘÁK, P. and MÁLEK, J.. Finanční matematika pro každého. 8. rozšířené vydání. Praha: Grada Publishing, a.s. 304 s. 2013. ISBN:078-80-247-4831-3. (CS)
Recommended reading
MACHÁČEK, O. Finanční a pojistná matematika: úrok a úročení, modely opakovaných plateb, burzovní operace při složeném úročení, pojistné operace. 2.vydání, Praha: Prospektrum. 213 s. 3001. ISBN 80-7175-104-9. (CS)
RADOVÁ, J. a kol. Finanční matematika pro každého, příklady + CD-ROM. 2. přepracované vydání.Praha: Grada publishing, a.s. 256 s. 2011. ISBN978-80-247-3584-9. (CS)
RADOVÁ, J. a kol. Finanční matematika pro každého, příklady + CD-ROM. 2. přepracované vydání.Praha: Grada publishing, a.s. 256 s. 2011. ISBN978-80-247-3584-9. (CS)
Classification of course in study plans
Type of course unit
Lecture
26 hod., optionally
Teacher / Lecturer
Syllabus
1. The organization and methods of teaching, course curriculum, assessment methods and criteria linked to outcomes. The repetition of necessary mathematical means: percentages, adjustment of expressions, solving equations, inequations, and their systems, functions, sequences and series, averages. Software support (for modeling, computations, visualizations, simulations). Motivation – selected comments from real financial environment.
2. Simple and compound interest, their combinations, discount, basic concepts, applications.
3. Interest – completion; Savings, basic concepts, types of saving – short-term, long-term, their combinations.
4. Time value of money – income tax, depreciation, value equation, time value, internal rate of return, payback period; Investment decision-making – criteria.
5. Pensions, basic concepts, current and final value of pension, types of pensions, special types of pensions.
6. Loans – annuity, amortization; Installment plan; Selected types of loans.
7. Bonds, basic concepts, types of bonds, price and rate of return to maturity of bond.
8. Shares, basic concepts, types of shares, share prices; Characteristics of bonds and shares – comparison.
9. Portfolio theory, financial risk, basic portfolio analysis - selected models; Investment and mutual funds in the Czech Republic.
10. Basics - Futures contracts; Speculation in securities; Currency rates.
11. Insurance – basics: insure mathematics, basic concepts, insurance risk, classification and types of insurance, classification of the insurance companies.
12. Applications – lecture from practice.
13. Reserve; Summary and preparation for exam.
2. Simple and compound interest, their combinations, discount, basic concepts, applications.
3. Interest – completion; Savings, basic concepts, types of saving – short-term, long-term, their combinations.
4. Time value of money – income tax, depreciation, value equation, time value, internal rate of return, payback period; Investment decision-making – criteria.
5. Pensions, basic concepts, current and final value of pension, types of pensions, special types of pensions.
6. Loans – annuity, amortization; Installment plan; Selected types of loans.
7. Bonds, basic concepts, types of bonds, price and rate of return to maturity of bond.
8. Shares, basic concepts, types of shares, share prices; Characteristics of bonds and shares – comparison.
9. Portfolio theory, financial risk, basic portfolio analysis - selected models; Investment and mutual funds in the Czech Republic.
10. Basics - Futures contracts; Speculation in securities; Currency rates.
11. Insurance – basics: insure mathematics, basic concepts, insurance risk, classification and types of insurance, classification of the insurance companies.
12. Applications – lecture from practice.
13. Reserve; Summary and preparation for exam.
Exercise
13 hod., compulsory
Teacher / Lecturer
Syllabus
1.-2. Teaching the exercises – organization, conditions of awarding the course-unit credit. Mathematical support – tasks. Software – example.
3.-4. Interest – tasks. Savings – tasks.
5.-6. Time value of money – tasks. Pensions – tasks.
7.-8. Loans + installment plan – tasks. Bonds + Shares – tasks.
9.-10. Portfolio theory – tasks. Currency rate – tasks.
11.-12. Credit test. Teaching completion.
13. Evaluation of the course. Unit credits.
3.-4. Interest – tasks. Savings – tasks.
5.-6. Time value of money – tasks. Pensions – tasks.
7.-8. Loans + installment plan – tasks. Bonds + Shares – tasks.
9.-10. Portfolio theory – tasks. Currency rate – tasks.
11.-12. Credit test. Teaching completion.
13. Evaluation of the course. Unit credits.