Financial and Insurance Mathematics

Coordinated by: Department of Probability and Mathematical Statistics
Study branch coordinator: doc. RNDr. Martin Branda, Ph.D.

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

CodeSubjectCreditsWinterSummer
NMFM401Mathematics of Non-Life Insurance 1 52/2 C+Ex
NMFM402Mathematics of Non-Life Insurance 2 52/2 C+Ex
NMFM404Selected Software Tools for Finance and Insurance 32/0 Ex
NMFM405Life Insurance 1 52/2 C+Ex
NMFM406Life Insurance 2 32/0 Ex
NMFM408Probability for Finance and Insurance 32/0 Ex
NMFM410Insurance Companies Accounting 52/2 C+Ex
NMFM416Life Insurance 2, exercises 20/2 C
NMFM501Seminar on Actuarial Sciences 1 20/2 C
NMFM502Seminar on Actuarial Sciences 2 10/2 C
NMFM503Risk Theory 84/2 C+Ex
NMFM505Stochastic Models for Finance and Insurance 52/2 C+Ex
NMFM507Advanced Topics of Financial Management 22/0 Ex
NMSA407Linear Regression 84/2 C+Ex
NMSA409Stochastic Processes 2 84/2 C+Ex
NMST537Time Series 84/2 C+Ex
NSZZ023Diploma Thesis I 60/4 C
NSZZ024Diploma Thesis II 90/6 C
NSZZ025Diploma Thesis III 150/10 C

8.2 Elective Courses

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

CodeSubjectCreditsWinterSummer
NMFM431Investment Analysis 52/2 C+Ex
NMFM531Financial Derivatives 1 32/0 Ex
NMFM532Financial Derivatives 2 32/0 Ex
NMSA403Optimisation Theory 52/2 C+Ex
NMST531Censored Data Analysis 52/2 C+Ex
NMST539Multivariate Analysis 52/2 C+Ex

Recommended Optional Courses

CodeSubjectCreditsWinterSummer
NMEK432Econometrics 84/2 C+Ex
NMEK532Optimisation with Applications to Finance 84/2 C+Ex
NMFM461Demography 32/0 Ex
NMFM462Practical Aspects of Financial Risk Measuring and Management 32/0 Ex
NMFM535Stochastic Analysis in Financial Mathematics 52/2 C+Ex
NMFM537Credit Risk in Banking 32/0 Ex
NMSA571Information Theory in Finance and Statistics 32/0 Ex
NMFP436Data Science 2 52/2 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

CodeSubjectCreditsWinterSummer
NMSA407Linear Regression 84/2 C+Ex
NMSA409Stochastic Processes 2 84/2 C+Ex
NMFM401Mathematics of Non-Life Insurance 1 52/2 C+Ex
NMFM405Life Insurance 1 52/2 C+Ex
NSZZ023Diploma Thesis I 60/4 C
NMFM402Mathematics of Non-Life Insurance 2 52/2 C+Ex
NMFM410Insurance Companies Accounting 52/2 C+Ex
NMFM404Selected Software Tools for Finance and Insurance 32/0 Ex
NMFM406Life Insurance 2 32/0 Ex
NMFM408Probability for Finance and Insurance 32/0 Ex
NMFM416Life Insurance 2, exercises 20/2 C
 Optional and Elective Courses 7  

2nd year

CodeSubjectCreditsWinterSummer
NSZZ024Diploma Thesis II 90/6 C
NMFM503Risk Theory 84/2 C+Ex
NMST537Time Series 84/2 C+Ex
NMFM501Seminar on Actuarial Sciences 1 20/2 C
NMFM505Stochastic Models for Finance and Insurance 52/2 C+Ex
NMFM507Advanced Topics of Financial Management 22/0 Ex
NSZZ025Diploma Thesis III 150/10 C
NMFM502Seminar on Actuarial Sciences 2 10/2 C
 Optional and Elective Courses 10