Financial and Insurance Mathematics
Coordinated by: Department of Probability and Mathematical Statistics
Study branch coordinator: doc. RNDr. Martin Branda, Ph.D.
The aim of the study program Financial and Insurance Mathematics is professional training in the profession of mathematician in financial institutions or for independent scientific activity in the fields of finance and insurance, including a possible academic career. Graduates of this study program will gain in-depth knowledge of basic mathematical disciplines and special knowledge of probability theory and mathematical statistics, econometrics and stochastic processes, mathematical methods in finance, life and non-life insurance, risk management, accounting (including insurance companies accounting) and machine learning. The teaching is largely based on mathematical modeling and advanced data analysis using modern software tools. All this allows graduates to perform highly effective modeling of financial and insurance products, their analysis in terms of risk, profitability and other characteristics necessary for effective financial management.
Graduates of the Financial and Insurance Mathematics study program will be employed in banks, insurance companies, pension and investment funds and other financial institutions, as well as in state administration (Ministry of Finance, Czech National Bank and others). The professions they then hold include actuaries, risk managers and data scientists. The current demand of the mentioned institutions for these professions, especially from the commercial sphere, is high and this trend will probably not change in the future. Last but not least, the graduates will receive the education that is the basis for the award of a certificate of competence to perform actuarial activities issued by the Czech Society of Actuaries to its members meeting the criteria of internationally recognized actuarial education (the certificate is valid for the entire EU).
Assumed Knowledge
It is assumed that an incoming student of this program has sufficient knowledge of the following topics and fields:
- –
Differential and integral calculus of one variable and
several variables. Measure theory. Lebesgue integral. Vector spaces,
matrix algebra.
- –Foundations of probability theory.
- –Foundations of mathematical statistics and data analysis, markov chain theory, linear regression.
- –Foundations of financial and actuarial mathematics.
- –Foundations of probability theory.
Should an incoming student not meet these entry requirements, the coordinator of the study program 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.
Study Plans
The study program has two study plans. The study plan N is intended for students who start their studies in the academic year 2022/2023 (or later). The study plan P is intended for students who started their studies in the academic year 2020/2021 or 2021/2022.
Financial and Insurance Mathematics, plan N
Study Plan N is intended for students who start their studies in the academic year 2022/2023 (or later).
Branch selection
Program Financial and Insurance Mathematics is splitted into two branches:
- 1. Branch Insurance mathmematics is designed for students who want to become actuaries or risk managers in insurance companies.
- 2. Branch Data science and finance is designed to prepare for careers in data science, advanced data analytics or risk management primarily in financial institutions.
Choosing a branch involves three sequential steps:
- – Selection of compulsory elective courses according to the recommended course of study, typically from the summer semester of the first year.
- – Selection of one of the two variants of the subject "Diploma Thesis III". This course is usually enrolled at the beginning of the last semester of study.
- – Selection of an optional topic of the oral part of the final exam, when registering for the final exam.
- – Selection of one of the two variants of the subject "Diploma Thesis III". This course is usually enrolled at the beginning of the last semester of study.
Choice of elective courses
The choice of compulsory elective courses is guided by the prerequisites of individual variants of the "Diploma Thesis III". Each variant requires the fulfillment of certain requirements for passing the courses of the chosen specialization. These prerequisites are not verified when enrolling in the course "Diploma Thesis III", so this course can be enrolled without meeting all the prerequisites. However, they are verified during the control of the fulfillment of study obligations, so that a student who does not meet the prerequisites of the subject "Diploma Thesis III" at this stage cannot complete the study.
Recommended Course of Study – Branch Insurance Mathematics
1st year
In the summer semester of the 1st year of study, it is necessary to choose one of two specializations and enroll in the corresponding elective courses according to it. The specific composition of the study plan continues in the second year.
| Code | Subject | Credits | Winter | Summer | |
| NMFP401 | Financial econometrics | 4 | 2/1 C+Ex | — | |
| NMFP403 | Stochastic Processes 2 | 8 | 4/2 C+Ex | — | |
| NMFP405 | Probability for Finance and Insurance | 4 | 2/1 C+Ex | — | |
| NMFP407 | Mathematics of Life Insurance 1 | 5 | 2/2 C+Ex | — | |
| NMFP409 | Mathematics of Non-Life Insurance 1 | 5 | 2/2 C+Ex | — | |
| NMFP402 | Generalized Linear Models | 5 | — | 2/2 C+Ex | |
| NMFP404 | Time Series | 8 | — | 4/2 C+Ex | |
| NMFP406 | Data Science 1 | 3 | — | 2/0 Ex | |
| NSZZ023 | Diploma Thesis I | 6 | — | 0/4 C | |
| NMFP432 | Mathematics of Life Insurance 2 | 5 | — | 2/2 C+Ex | |
| NMFP434 | Mathematics of Non-Life Insurance 2 | 5 | — | 2/2 C+Ex | |
| Optional and Elective courses | 2 | ||||
2nd year
| Code | Subject | Credits | Winter | Summer | |
| NMFP501 | Seminar on Actuarial Science 1 | 2 | 0/2 C | — | |
| NMFP503 | Risk Theory 1 | 4 | 2/1 C+Ex | — | |
| NMFP505 | Stochastic Models in Finance 1 | 5 | 2/2 C+Ex | — | |
| NMFP531 | Risk Theory 2 | 4 | 2/1 C+Ex | — | |
| NMFP537 | Accounting and Solvency of Insurance Companies | 5 | 2/2 C+Ex | — | |
| NSZZ024 | Diploma Thesis II | 9 | — | 0/6 C | |
| NMFP532 | Seminar on Actuarial Science 2 | 2 | — | 0/2 C | |
| NMFP558 | Diploma Thesis III in Actuarial Mathematics | 15 | — | 0/10 C | |
| Optional and Elective courses | 14 | ||||
Recommended Course of Study – Branch Data Science and Finance
1st year
In the summer semester of the 1st year of study, it is necessary to choose one of two specializations and enroll in the corresponding elective courses according to it. The specific composition of the study plan continues in the second year.
| Code | Subject | Credits | Winter | Summer | |
| NMFP401 | Financial econometrics | 4 | 2/1 C+Ex | — | |
| NMFP403 | Stochastic Processes 2 | 8 | 4/2 C+Ex | — | |
| NMFP405 | Probability for Finance and Insurance | 4 | 2/1 C+Ex | — | |
| NMFP407 | Mathematics of Life Insurance 1 | 5 | 2/2 C+Ex | — | |
| NMFP409 | Mathematics of Non-Life Insurance 1 | 5 | 2/2 C+Ex | — | |
| NMFP402 | Generalized Linear Models | 5 | — | 2/2 C+Ex | |
| NMFP404 | Time Series | 8 | — | 4/2 C+Ex | |
| NMFP406 | Data Science 1 | 3 | — | 2/0 Ex | |
| NSZZ023 | Diploma Thesis I | 6 | — | 0/4 C | |
| NMEK412 | Optimisation with Applications to Finance | 5 | — | 2/2 C+Ex | |
| NMFP436 | Data Science 2 | 5 | — | 2/2 C+Ex | |
| Optional and Elective courses | 2 | ||||
2nd year
| Code | Subject | Credits | Winter | Summer | |
| NMFP501 | Seminar on Actuarial Science 1 | 2 | 0/2 C | — | |
| NMFP503 | Risk Theory 1 | 4 | 2/1 C+Ex | — | |
| NMFP505 | Stochastic Models in Finance 1 | 5 | 2/2 C+Ex | — | |
| NMFP533 | Investment Analysis | 5 | 2/2 C+Ex | — | |
| NMFP535 | Data Science 3 | 5 | 2/2 C+Ex | — | |
| NSZZ024 | Diploma Thesis II | 9 | — | 0/6 C | |
| NMFP534 | Stochastic Models in Finance 2 | 3 | — | 2/0 Ex | |
| NMFP556 | Diploma Thesis III in finance | 15 | — | 0/10 C | |
| Optional and Elective courses | 12 | ||||
Summary of the Study Plan
Obligatory Courses
All courses in this group must be successfully completed.
| Code | Subject | Credits | Winter | Summer | |
| NMFP401 | Financial econometrics | 4 | 2/1 C+Ex | — | |
| NMFP403 | Stochastic Processes 2 | 8 | 4/2 C+Ex | — | |
| NMFP405 | Probability for Finance and Insurance | 4 | 2/1 C+Ex | — | |
| NMFP407 | Mathematics of Life Insurance 1 | 5 | 2/2 C+Ex | — | |
| NMFP409 | Mathematics of Non-Life Insurance 1 | 5 | 2/2 C+Ex | — | |
| NMFP402 | Generalized Linear Models | 5 | — | 2/2 C+Ex | |
| NMFP404 | Time Series | 8 | — | 4/2 C+Ex | |
| NMFP406 | Data Science 1 | 3 | — | 2/0 Ex | |
| NSZZ023 | Diploma Thesis I | 6 | — | 0/4 C | |
| NMFP501 | Seminar on Actuarial Science 1 | 2 | 0/2 C | — | |
| NMFP503 | Risk Theory 1 | 4 | 2/1 C+Ex | — | |
| NMFP505 | Stochastic Models in Finance 1 | 5 | 2/2 C+Ex | — | |
| NSZZ024 | Diploma Thesis II | 9 | — | 0/6 C | |
Elective courses
At least 21 credits must be obtained by passing the elective courses.
Branch Insurance Mathematics
The choice of compulsory elective courses in Insurance Mathematics is determined by the prerequisites of the course "Diploma Thesis III in Insurance Mathematics", which requires the completion of all of these courses:
| Code | Subject | Credits | Winter | Summer | |
| NMFP432 | Mathematics of Life Insurance 2 | 5 | — | 2/2 C+Ex | |
| NMFP434 | Mathematics of Non-Life Insurance 2 | 5 | — | 2/2 C+Ex | |
| NMFP531 | Risk Theory 2 | 4 | 2/1 C+Ex | — | |
| NMFP537 | Accounting and Solvency of Insurance Companies | 5 | 2/2 C+Ex | — | |
| NMFP532 | Seminar on Actuarial Science 2 | 2 | — | 0/2 C | |
Branch Data Science and Finance
The choice of compulsory elective courses in Data Science and Finance is determined by the prerequisites of the course "Diploma Thesis III in Finance", which requires the completion of all of these courses:
| Code | Subject | Credits | Winter | Summer | |
| NMEK412 | Optimisation with Applications to Finance | 5 | — | 2/2 C+Ex | |
| NMFP436 | Data Science 2 | 5 | — | 2/2 C+Ex | |
| NMFP533 | Investment Analysis | 5 | 2/2 C+Ex | — | |
| NMFP535 | Data Science 3 | 5 | 2/2 C+Ex | — | |
| NMFP534 | Stochastic Models in Finance 2 | 3 | — | 2/0 Ex | |
Recommended Optional Courses
Not only this list serves as recommended optional courses, but students of the given branch can use elective courses of the second branch as optional courses.
| Code | Subject | Credits | Winter | Summer | |
| NMFP461 | Credit Risk in Banking | 3 | 2/0 Ex | — | |
| NMFP465 | Financial Derivatives 1 | 3 | 2/0 Ex | — | |
| NMSA413 | Optimisation Theory | 8 | 4/2 C+Ex | — | |
| NPFL129 | Introduction to Machine Learning with Python | 5 | 2/2 C+Ex | — | |
| NMEK436 | Computational Aspects of Optimisation | 5 | — | 2/2 C+Ex | |
| NMFP462 | Demography | 3 | — | 2/0 Ex | |
| NMEK531 | Mathematical Economics | 5 | 2/2 C+Ex | — | |
| NMFP463 | Practical Aspects of Financial Risk Measuring and Management | 3 | 2/0 Ex | — | |
| NMFP466 | Financial Derivatives 2 | 3 | 2/0 Ex | — | |
State Final Exam
Requirements for taking the last part of the final exam
- – Earning at least 120 credits during the course of the study.
- – Completion of all obligatory courses prescribed by the study plan.
- – Completion of all elective courses prescribed by the study branch.
- – Submission of a completed Master's Thesis by the submission deadline.
- – Completion of all obligatory courses prescribed by the study plan.
Requirements for taking other than the last part of the final exam
General rules are set in the internal regulation Rules Of Study at the Faculty. In the program Mathematical structures, the following are required:
- – Earning at least 105 credits during the course of the study.
- – If the other than the last part of the final exam is the oral part, completion of all obligatory courses prescribed by the study plan and all elective courses prescribed by the study branch except for Diploma Thesis III (NMFP556 or NMFP558 according to the study branch) is required.
- – If the other than the last part of the final exam is the defence, completion of all obligatory courses prescribed by the study plan and all elective courses prescribed by the study branch and submission of a completed Master's Thesis by the submission deadline are required.
- – If the other than the last part of the final exam is the oral part, completion of all obligatory courses prescribed by the study plan and all elective courses prescribed by the study branch except for Diploma Thesis III (NMFP556 or NMFP558 according to the study branch) is required.
Oral part of the final exam
The oral part of the final exam consists of three subject areas, from each the student gets one question. Two areas (Fundamentals of Probability, Mathematical Statistics and Econometrics; Fundamentals of Financial and Actuarial Mathematics) are compulsory, the third area is optional and corresponds to the chosen branch of study. The student can choose the third area:
- – Advanced Topics of Actuarial Mathematics and Accounting of Insurance Companies (corresponds to the branch Insurance Mathematics)
- – Advanced Topics of Finance and Data Analysis (corresponds to the branch Data Science and Finance)
A more detailed explanation of the requirements for the oral part of the final exam can be found on the website of the program guarantor: https://www2.karlin.mff.cuni.cz/~branda/garantfpm.html.
Requirements for the oral part of the final exam
1. Fundamentals of Probability, Mathematical Statistics and Econometrics
Probability for finance and insurance, econometric models, stochastic processes and time series, generalized linear models.
2. Fundamentals of Financial and Actuarial Mathematics
Fundamentals of life and non-life actuarial mathematics, risk theory, basic stochastic models in finance.
3. Optional areas
3A. Advanced Topics of Actuarial Mathematics and Accounting of Insurance Companies
Advanced topics of life and non-life actuarial mathematics, risk theory, accounting and solvency of insurance companies.
3B. Advanced Topics of Finance and Data Analysis
Optimization models with application in finance, investment analysis and models, risk measures, advanced stochastic models in finance, multivariate statistical models.
Financial and Insurance Mathematics, plan P
Study Plan P is intended for students who start their studies in the academic year 2020/2021 or 2021/2022. In the recommended course of study, it is necessary to pay attention to the following marked changes:
- – Most courses are no longer taught. For these courses, it is stated which new courses replace these non-taught ones.
- – The semester of some courses has changed.
Recommended Course of Study
1st year
| Code | Subject | Credits | Winter | Summer | |
| NMFM401 | Mathematics of Non-Life Insurance 1 | 1 | 5 | 2/2 C+Ex | — |
| NMFM405 | Life Insurance 1 | 2 | 5 | 2/2 C+Ex | — |
| NMSA407 | Linear Regression | 8 | 4/2 C+Ex | — | |
| NMSA409 | Stochastic Processes 2 | 8 | 4/2 C+Ex | — | |
| NMFM402 | Mathematics of Non-Life Insurance 2 | 3 | 5 | — | 2/2 C+Ex |
| NMFM404 | Selected Software Tools for Finance and Insurance | 4 | 3 | — | 2/0 Ex |
| NMFM406 | Life Insurance 2 | 5 | 3 | — | 2/0 Ex |
| NMFM416 | Life Insurance 2, exercises | 5 | 2 | — | 0/2 C |
| NMFM408 | Probability for Finance and Insurance | 6 | 3 | — | 2/0 Ex |
| NMFM410 | Insurance Companies Accounting | 7 | 5 | — | 2/2 C+Ex |
| NSZZ023 | Diploma Thesis I | 6 | — | 0/4 C | |
| Optional and Elective courses | 7 | ||||
1This course is no longer taught. It is replaced by a course NMFP409 Mathematics of Non-life Insurance 1.
2 This course is no longer taught. It is replaced by a course NMFP407 Mathematics of Life Insurance 1.
3 This course is no longer taught. It is replaced by a course NMFP434 Mathematics of Non-life Insurance 2.
4 This course is no longer taught. It is replaced by a course NMFP406 Data Science 1.
5 This courses are no longer taught. They are replaced by a course NMFP432 Mathematics of Life Insurance 2 (2/2 Z+Zk).
6 This course is no longer taught. It is replaced by a course taught in the winter semester NMFP405 Probability for Finance and Insurance (2/1 C+Ex).
7 This course is no longer taught. It is replaced by a course taught in the winter semester NMFP537 Accounting and Solvency of Insurance Companies.
2nd year
| Code | Subject | Credits | Winter | Summer | |
| NMFM501 | Seminar on Actuarial Sciences 1 | 8 | 2 | 0/2 C | — |
| NMFM503 | Risk Theory | 9 | 8 | 4/2 C+Ex | — |
| NMFM507 | Advanced Topics of Financial Management | 10 | 2 | 2/0 Ex | — |
| NMST537 | Time Series | 11 | 8 | 4/2 C+Ex | — |
| NSZZ024 | Diploma Thesis II | 9 | 0/6 C | — | |
| NMFM502 | Seminar on Actuarial Sciences 2 | 12 | 1 | — | 0/2 C |
| NMFM505 | Stochastic Models for Finance and Insurance | 13 | 5 | — | 2/2 C+Ex |
| NSZZ025 | Diploma Thesis III | 15 | — | 0/10 C | |
| Optional and Elective courses | 10 | ||||
8This course is no longer taught. It is replaced by a course NMFP501 Seminar on Actuarial Sciences 1.
9This course is no longer taught. It is replaced by courses NMFP503 Risk Theory 1 (2/1 Z+Zk) a NMFP531 Risk Theory 2 (2/1 Z+Zk).
10This course is no longer taught. It is replaced by a course NMFP533 Investment Analysis.
11 This course is no longer taught. It is replaced by a course taught in the summer semester NMFP404 Time Series.
12This course is no longer taught. It is replaced by a course NMFP532 Seminar on Actuarial Sciences 2.
13This course is no longer taught. It is replaced by a course NMFP505 Stochastic Models in Finance 1.
Summary of the Study Plan
Obligatory Courses
| Code | Subject | Credits | Winter | Summer | |
| NMFM401 | Mathematics of Non-Life Insurance 1 | 1 | 5 | 2/2 C+Ex | — |
| NMSA407 | Linear Regression | 8 | 4/2 C+Ex | — | |
| NMFM405 | Life Insurance 1 | 2 | 5 | 2/2 C+Ex | — |
| NMSA409 | Stochastic Processes 2 | 8 | 4/2 C+Ex | — | |
| NMFM402 | Mathematics of Non-Life Insurance 2 | 3 | 5 | — | 2/2 C+Ex |
| NMFM404 | Selected Software Tools for Finance and Insurance | 4 | 3 | — | 2/0 Ex |
| NMFM406 | Life Insurance 2 | 5 | 3 | — | 2/0 Ex |
| NMFM416 | Life Insurance 2, exercises | 5 | 2 | — | 0/2 C |
| NMFM408 | Probability for Finance and Insurance | 6 | 3 | — | 2/0 Ex |
| NMFM410 | Insurance Companies Accounting | 7 | 5 | — | 2/2 C+Ex |
| NMFM501 | Seminar on Actuarial Sciences 1 | 8 | 2 | 0/2 C | — |
| NMFM503 | Risk Theory | 9 | 8 | 4/2 C+Ex | — |
| NMFM507 | Advanced Topics of Financial Management | 10 | 2 | 2/0 Ex | — |
| NMST537 | Time Series | 11 | 8 | 4/2 C+Ex | — |
| NMFM502 | Seminar on Actuarial Sciences 2 | 12 | 1 | — | 0/2 C |
| NMFM505 | Stochastic Models for Finance and Insurance | 13 | 5 | — | 2/2 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 | |
1This course is no longer taught. It is replaced by a course NMFP409 Mathematics of Non-life Insurance 1.
2 This course is no longer taught. It is replaced by a course NMFP407 Mathematics of Life Insurance 1.
3 This course is no longer taught. It is replaced by a course NMFP434 Mathematics of Non-life Insurance 2.
4 This course is no longer taught. It is replaced by a course NMFP406 Data Science 1.
5 This courses are no longer taught. They are replaced by a course NMFP432 Mathematics of Life Insurance 2 (2/2 Z+Zk).
6 This course is no longer taught. It is replaced by a course taught in the winter semester NMFP405 Probability for Finance and Insurance (2/1 C+Ex).
7 This course is no longer taught. It is replaced by a course taught in the winter semester NMFP537 Accounting and Solvency of Insurance Companies.
8This course is no longer taught. It is replaced by a course NMFP501 Seminar on Actuarial Sciences 1.
9This course is no longer taught. It is replaced by courses NMFP503 Risk Theory 1 (2/1 Z+Zk) a NMFP531 Risk Theory 2 (2/1 Z+Zk).
10This course is no longer taught. It is replaced by a course NMFP533 Investment Analysis.
11This course is no longer taught. It is replaced by a course taught in the summer semester NMFP404 Time Series.
12This course is no longer taught. It is replaced by a course NMFP532 Seminar on Actuarial Sciences 2.
13This course is no longer taught. It is replaced by a course NMFP505 Stochastic Models in Finance 1.
Elective Courses
It is necessary to obtain at least 5 credits from elective courses.
| Code | Subject | Credits | Winter | Summer | |
| NMFM431 | Investment Analysis | 5 | 2/2 C+Ex | — | |
| NMFM531 | Financial Derivatives 1 | 1 | 3 | 2/0 Ex | — |
| NMFM532 | Financial Derivatives 2 | 2 | 3 | 2/0 Ex | — |
| NMSA403 | Optimisation Theory | 3 | 5 | 2/2 C+Ex | — |
| NMST531 | Censored Data Analysis | 5 | 2/2 C+Ex | — | |
| NMST539 | Multivariate Analysis | 4 | 5 | 2/2 C+Ex | — |
1 This course is no longer taught. It is replaced by a course NMFP465 Financial Derivatives 1.
2 This course is no longer taught. It is replaced by a course NMFP466 Financial Derivatives 2.
3 This course is no longer taught. It is replaced by a course NMSA413 Optimization Theory (4/2 C+Ex).
4 This course is no longer taught. It is replaced by a course NMFP535 Data Science 3.
Recommended Optional Courses
| Code | Subject | Credits | Winter | Summer | |
| NMEK432 | Econometrics | 1 | 8 | — | 4/2 C+Ex |
| NMEK532 | Optimisation with Applications to Finance | 2 | 8 | — | 4/2 C+Ex |
| NMFM461 | Demography | 3 | 3 | — | 2/0 Ex |
| NMFM462 | Practical Aspects of Financial Risk Measuring and Management | 4 | 3 | 2/0 Ex | — |
| NMFM537 | Credit Risk in Banking | 5 | 3 | 2/0 Ex | — |
| NMFP436 | Data Science 2 | 5 | — | 2/2 C+Ex | |
| NMFP534 | Stochastic Models in Finance 2 | 3 | — | 2/0 Ex | |
1 This course is no longer taught. It can replaced by courses taught in the winter semester NMFP401 Financial Econometrics (2/1 C+Ex) or NMEK511 Econometrics (4/2 C+Ex).
2 This course is no longer taught. It is replaced by a course NMEK412 Optimisation with Applications to Finance (2/2 C+Ex).
3 This course is no longer taught. It is replaced by a course NMFP462 Demography.
4 This course is no longer taught. It is replaced by a course NMFP463 Practical Aspects of Financial Risk Measuring and Management.
5 This course is no longer taught. It is replaced by a course NMFP461 Credit Risk in Banking.
State Final Exam
Requirements for taking the final exam
Requirements for taking the last part of 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.
- – Completion of all obligatory courses prescribed by the study plan.
Requirements for taking other than the last part of the final exam
General rules are set in the internal regulation Rules Of Study at the Faculty. In the program Mathematical structures, the following are required:
- – Earning at least 105 credits during the course of the study.
- – If the other than the last part of the final exam is the oral part, completion of all obligatory courses prescribed by the study plan except for NSZZ025 Diploma Thesis III is required.
- – If the other than the last part of the final exam is the defence, completion of all obligatory courses prescribed by the study plan and submission of a completed Master's Thesis by the submission deadline are required.
- – Earning at least 5 credits by completion of elective courses.
- – If the other than the last part of the final exam is the oral part, completion of all obligatory courses prescribed by the study plan except for NSZZ025 Diploma Thesis III is required.
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. Applied Probability
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. Stochastic models in finance. Financial risk and its measuring. Stock market analysis. Accounting.
