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Main menu for Browse IS/STAG
Course info
KMA / FIPM
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Course description
Department/Unit / Abbreviation
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KMA
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FIPM
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Mathematics for Finance and Insurance
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
5
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
3
[Hours/Week]
Seminar
1
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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Czech
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Occ/max
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Automatic acceptance of credit before examination
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No
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Summer semester
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0 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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8 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Winter + Summer
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Semester taught
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Winter + Summer
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Minimum (B + C) students
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1
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
No
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Fundamental course |
No
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Fundamental theoretical course |
No
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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None
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Preclusive courses
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KSO/FIPV
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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KMA/ASF
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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To present mathematical methods used in the field of financial mathematics with discrete time and life insurance (interest, time value of money, cash flows, annuities, investment decisions, internal rate of return, duration, loan redemption; calculations associated with bonds, portfolio analysis; introduction to actuarial mathematics, life insurance premiums and reserves).
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Requirements on student
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FOR WINTER SEMESTER OF SCHOOL YEAR 2023/2024
Knowledge and understanding of lectures and ability to apply it to the examples.
Upon repeated registration of the course, the credit obtained in the previous study of this course is not recognized.
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Content
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FOR WINTER SEMESTER OF SCHOOL YEAR 2023/2024
Introduction - simple and compound interest. Interest rate and discount rate. Nominal interest rate. Time value of money. Effective interest rate and nominal interest and discount rate. Present value, discrete cash flow.
Annuities - annuity in arrears and annuity in advance ? present and future value. More payment in one period, postponed annuity.
Investment decisions according to present value, payback period. Internal rate of return, inflation.
Funds - rate of profit. Duration.
Debt payment - sum payable, principal and interest payment. Constant repayment.
Bonds - bond and its price, yield to redemption, duration.
Portfolio analysis. Expected return and its risk. Markowitz model, tangency portfolio. Capital asset pricing model (CAPM), market portfolio, CML.
Life tables. Single-decrement population life table, types of life tables, balancing. Technical interest rate, commutation-columns numbers. Life insurance. Endowment insurance, death insurance, mixed insurance, pension insurance and their present value. Equivalence principle, net premium. Operating expenses, gross premium. Reserves in life insurance. Net reserve, risk and deposit part. Gross reserve, surrender, changes within insurance.
Additional information on the web page https://home.zcu.cz/~friesl/Vyuka/Fipm.html
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Recommended:
Mc Cutcheon, J.J., Scott, W.F. An Introduction to the Mathematics of Finance. 1991.
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Recommended:
Blake, David. Analýza finančních trhů. 1. vyd. Praha : Grada, 1995. ISBN 80-7169-201-8.
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Recommended:
Friesl, Michal; Šedivá, Blanka. Finanční matematika hypertextově. Plzeň : Západočeská univerzita, 2003.
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Recommended:
Finanční matematika hypertextově, verze 2003-12-31
(Friesl, M., Šedivá, B.)
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Recommended:
Cipra, Tomáš. Finanční matematika v praxi. 1. vydání. Praha : Nakladatelství HZ, 1997. ISBN 80-901495-1-0.
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Recommended:
Macro-Investment Analysis
(Sharpe, W.F.)
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Recommended:
CIPRA, T. Praktický průvodce finanční a pojistnou matematikou. Praha : HZ, 1995.
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Recommended:
BRADA, J. Teorie portfolia. 1. vyd. Praha : Vysoká škola ekonomická, 1996. ISBN 80-7079-259-0.
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Recommended:
Walter J., Radová J. Základy finanční a pojistné matematiky. Praha, 1995.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Contact hours
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52
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Preparation for formative assessments (2-20)
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26
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Preparation for an examination (30-60)
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40
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Undergraduate study programme term essay (20-40)
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16
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Total
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134
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
proficiency in secondary-school mathematics (arithmetic and geometric sequence and their sums, linear, power, exponential, logarthmic functions and their properties, equations and inequalities, linear interpolation ...) |
basic linear algebra (matrix multiplication) and differential calculus |
Prior completion of a basic course of probability (probability, random variable, expectation, variance, covariance, correlation coefficient) |
general awareness of financial concepts (stocks, bonds, insurance, savings, etc.) |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
proficiency in secondary-school mathematics (arithmetic and geometric sequence and their sums, linear, power, exponential, logarthmic functions and their properties, equations and inequalities, linear interpolation ...) |
basic linear algebra (matrix multiplication) and differential calculus |
and above all the ability to think |
Prior completion of a basic course of probability (probability, random variable, expectation, variance, covariance, correlation coefficient) |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
to make use of mostly secondary-school mathematics to solve problems in treated areas of financial mathematics and life insurance |
Skills - skills resulting from the course: |
to make use of mostly secondary-school mathematics to solve problems in treated areas of financial mathematics and life insurance |
Competences - competences resulting from the course: |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Skills demonstration during practicum |
Seminar work |
Skills - skills achieved by taking this course are verified by the following means: |
Seminar work |
Combined exam |
Skills demonstration during practicum |
Competences - competence achieved by taking this course are verified by the following means: |
Seminar work |
Combined exam |
Skills demonstration during practicum |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Task-based study method |
Skills demonstration |
Group discussion |
Self-study of literature |
Individual study |
One-to-One tutorial |
Interactive lecture |
Discussion |
Skills - the following training methods are used to achieve the required skills: |
Interactive lecture |
Discussion |
One-to-One tutorial |
Group discussion |
Skills demonstration |
Task-based study method |
Individual study |
Self-study of literature |
Competences - the following training methods are used to achieve the required competences: |
Interactive lecture |
Discussion |
One-to-One tutorial |
Group discussion |
Skills demonstration |
Task-based study method |
Individual study |
Self-study of literature |
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