Course: Mathematics for Finance and Insurance

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Course title Mathematics for Finance and Insurance
Course code KMA/FIPM
Organizational form of instruction Lecture + Seminar
Level of course Bachelor
Year of study not specified
Semester Winter and summer
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • Friesl Michal, Mgr. Ph.D.
  • Marek Patrice, Ing. Ph.D.
  • Tomiczková Světlana, RNDr. Ph.D.
Course content
FOR WINTER SEMESTER OF SCHOOL YEAR 2017/2018 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

Learning activities and teaching methods
Lecture with practical applications, Discussion, One-to-One tutorial, Group discussion, Skills demonstration, Task-based study method, Individual study, Students' self-study, Self-study of literature
  • Contact hours - 52 hours per semester
  • Undergraduate study programme term essay (20-40) - 16 hours per semester
  • Preparation for an examination (30-60) - 40 hours per semester
  • Preparation for formative assessments (2-20) - 26 hours per semester
professional knowledge
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) and general awareness of financial concepts (stocks, bonds, insurance, savings, etc.) is appropriate.
learning outcomes
To use mostly secondary-school mathematics to solve problems in treated areas of financial mathematics and life insurance.
teaching methods
Task-based study method
Skills demonstration
Group discussion
Students' self-study
Self-study of literature
Individual study
One-to-One tutorial
Lecture with practical applications
assessment methods
Combined exam
Skills demonstration during practicum
Seminar work
Recommended literature
  • Blake, David. Analýza finančních trhů. 1. vyd. Praha : Grada, 1995. ISBN 80-7169-201-8.
  • BRADA, J. Teorie portfolia. 1. vyd. Praha : Vysoká škola ekonomická, 1996. ISBN 80-7079-259-0.
  • CIPRA, T. Praktický průvodce finanční a pojistnou matematikou. Praha : HZ, 1995.
  • Cipra, Tomáš. Finanční matematika v praxi. 1. vydání. Praha : Nakladatelství HZ, 1997. ISBN 80-901495-1-0.
  • Friesl, Michal; Šedivá, Blanka. Finanční matematika hypertextově. Plzeň : Západočeská univerzita, 2003.
  • Mc Cutcheon, J.J., Scott, W.F. An Introduction to the Mathematics of Finance. 1991.
  • Walter J., Radová J. Základy finanční a pojistné matematiky. Praha, 1995.

Study plans that include the course