8 Degree Plans – Financial and Insurance Mathematics

Coordinated by: Department of Probability and Mathematical Statistics
Study branch coordinator: prof. RNDr. Tomáš Cipra, DrSc.

This programme provides theoretical and applied education in financial and insurance mathematics. A solid mathematical background provides the foundations for developing disciplines of mathematical modelling in the insurance and banking industry and other financial areas. The graduate will be able to develop financial and insurance products and analyse their profitability and risk.

The graduate will have a deep knowledge of basic mathematical disciplines (mathematical analysis, algebra) and special knowledge in the fields of probability and statistics, stochastic processes, mathematical methods in finance, life and non-life insurance, advanced financial management, risk theory, accounting, and modelling with progressive systems (Mathematica). This knowledge provides tools for effective modelling of financial and insurance products, analysis of their profitability and risk, and other characteristics important for effective financial management.

Assumed knowledge

It is assumed that an incoming student of this branch has sufficient knowledge of the following topics and fields:

Multivariate differential and integral calculus, measure theory, Lebesgue integral, vector spaces, matrix algebra.
Foundations of probability theory, mathematical statistics, and data analysis. Theory of Markov chains.
Foundations of financial mathematics and accounting.
Foundations of functional programming.

Should an incoming student not meet these entry requirements, the coordinator of the study programme may assign a method of acquiring the necessary knowledge and abilities, which may for example mean taking selected bachelor's courses, taking a reading course with an instructor, or following tutored independent study.

8.1 Obligatory Courses

Code Subject Credits Winter Summer
NMFM401 Mathematics of Non-Life Insurance 1   5 2/2 C+Ex
NMFM402 Mathematics of Non-Life Insurance 2   5 2/2 C+Ex
NMFM404 Selected Software Tools for Finance and Insurance   3 2/0 Ex
NMFM405 Life Insurance 1   5 2/2 C+Ex
NMFM406 Life Insurance 2   3 2/0 Ex
NMFM408 Probability for Finance and Insurance   3 2/0 Ex
NMFM410 Insurance Companies Accounting   5 2/2 C+Ex
NMFM416 Life Insurance 2, exercises   2 0/2 C
NMFM501 Seminar on Actuarial Sciences 1   2 0/2 C
NMFM502 Seminar on Actuarial Sciences 2   1 0/2 C
NMFM503 Risk Theory   8 4/2 C+Ex
NMFM505 Stochastic Models for Finance and Insurance   5 2/2 C+Ex
NMFM507 Advanced Topics of Financial Management   2 2/0 Ex
NMSA407 Linear Regression   8 4/2 C+Ex
NMSA409 Stochastic Processes 2   8 4/2 C+Ex
NMST537 Time Series   8 4/2 C+Ex
NSZZ023 Diploma Thesis I   6 0/4 C
NSZZ024 Diploma Thesis II   9 0/6 C
NSZZ025 Diploma Thesis III   15 0/10 C

8.2 Elective Courses

It is required to earn at least 5 credits from the following elective courses.

Code Subject Credits Winter Summer
NMFM431 Investment Analysis   5 2/2 C+Ex
NMFM531 Financial Derivatives 1   3 2/0 Ex
NMFM532 Financial Derivatives 2   3 2/0 Ex
NMSA403 Optimisation Theory   5 2/2 C+Ex
NMST531 Censored Data Analysis   5 2/2 C+Ex
NMST539 Multivariate Analysis   5 2/2 C+Ex

Recommended Optional Courses

Code Subject Credits Winter Summer
NMEK432 Econometrics   8 4/2 C+Ex
NMFM462 Practical Aspects of Financial Risk Measuring and Management   3 2/0 Ex
NMFM535 Stochastic Analysis in Financial Mathematics   5 2/2 C+Ex

8.3 State Final Exam

Requirements for taking the final exam

 Earning at least 120 credits during the course of the study.
 Completion of all obligatory courses prescribed by the study plan.
 Earning at least 5 credits by completion of elective courses.
 Submission of a completed master's thesis by the submission deadline.

Oral part of the state final exam

The oral part of the final exam consists of three subject areas: ''Applied Probability", ''Insurance", and ''Finance and Accounting". One question is asked from each subject area.

Requirements for the oral part of the final exam

1. Probability and Statistics

Random variables, characteristics of their distributions. Random vectors, joint distribution, covariance, correlation, dependence modelling and measurement. Conditional distribution. Probability distributions in financial mathematics. Parameter estimators and their properties. Confidence intervals. Hypothesis testing principles. Maximum likelihood principle and the method of moments. One-sample, two-sample, paired tests. Analysis of variance. Linear regression model. The Bayes principle. Laws of large numbers and central limit theorems. Markov chains. Stationary processes. Time Series. Credibility theory. Collective risk models. Essentials of stochastic analysis.

2. Insurance

Demographic model of life insurance. Capital and life policies. Reserves of life insurance. Multiple decrement models. Multiple life insurance. Solvency and reinsurance. Technical reserves of general insurance. Tariff rates.

3. Finance and Accounting

Foundations of finance. Securities and their pricing. Financial risk. Stock market analysis. Accounting.

8.4 Recommended Course of Study

1st year

Code Subject Credits Winter Summer
NMSA407 Linear Regression   8 4/2 C+Ex
NMSA409 Stochastic Processes 2   8 4/2 C+Ex
NMFM401 Mathematics of Non-Life Insurance 1   5 2/2 C+Ex
NMFM405 Life Insurance 1   5 2/2 C+Ex
NSZZ023 Diploma Thesis I   6 0/4 C
NMFM402 Mathematics of Non-Life Insurance 2   5 2/2 C+Ex
NMFM410 Insurance Companies Accounting   5 2/2 C+Ex
NMFM404 Selected Software Tools for Finance and Insurance   3 2/0 Ex
NMFM406 Life Insurance 2   3 2/0 Ex
NMFM408 Probability for Finance and Insurance   3 2/0 Ex
NMFM416 Life Insurance 2, exercises   2 0/2 C
  Optional and Elective Courses   7    

2nd year

Code Subject Credits Winter Summer
NSZZ024 Diploma Thesis II   9 0/6 C
NMFM503 Risk Theory   8 4/2 C+Ex
NMST537 Time Series   8 4/2 C+Ex
NMFM501 Seminar on Actuarial Sciences 1   2 0/2 C
NMFM505 Stochastic Models for Finance and Insurance   5 2/2 C+Ex
NMFM507 Advanced Topics of Financial Management   2 2/0 Ex
NSZZ025 Diploma Thesis III   15 0/10 C
NMFM502 Seminar on Actuarial Sciences 2   1 0/2 C
  Optional and Elective Courses   10