Mathematical Foundations of Risk Analysis
ÚSI-RSMATAcad. year: 2020/2021
The course concerns mathematical modelling and its applications in risk engineering. It explains fundamental ideas and notions, especially by means of suitable examples, and deals with their applicability and a unifying view of mathematical principles. Related mathematical methods for achieving solutions in individual areas will be presented with the use of suitable software: Statistics, Minitab, Matlab and Excel.
Learning outcomes of the course unit
Fundamental concepts, methods and analytical techniques related to risk modelling will be studied. Specific ways of reasoning that are typical for risk analysis and related model building will be developed and enhanced.
Basic knowledge of undergraduate mathematics (linear algebra, differential and integral calculus, probability and statistics, numerical methods), and computer technology for use with application software.
Recommended optional programme components
Recommended or required reading
ANDĚL, Jiří. Základy matematické statistiky. Praha: Matfyzpress, 2011. ISBN 978-80-7378-162-0. (CS)
KARPÍŠEK, Zdeněk. MATEMATIKA IV: Statistika a pravděpodobnost. Akademické nakladatelství CERM s.r.o., Brno 2014. ISBN 978-80-214-4858-2.
CIPRA, Tomáš. Riziko ve financích a pojišťovnictví: Basel III a Solvency II. Ekopress 2015. ISBN 978-80-87865-24-8.
AGRESTI, Alan. Categorical Data Analysis. 3rd ed. New York: John Wiley & Sons, 2013. ISBN 0-470-46363-5.
BROCKWELL, Peter J., DAVIS, Richard, A. Introduction to Time Series and Forecasting. 2nd ed. New York: Springer-Verlag, 2002. ISBN 0-387-95351-5
Manuály software Statistica, Minitab, Matlab, Excel.
KLIR, George J., YUAN, Bo. Fuzzy Sets and Fuzzy Logic - Theory and Applications. New Jersey: Prentice Hall, 1995.
MONTGOMERY, Douglas C., RUNGER, George. Applied Statistics and Probability for Engineers. 5th ed. New York: John Wiley & Sons, 2010. ISBN 978-0-470-05304-1. (CS)
Planned learning activities and teaching methods
Tuition takes place via lectures and seminars. The lectures focus on the explanation of basic principles, the methods of the given discipline, problems and example solutions. The seminars mainly support practical mastery of the subject matter presented in lectures or assigned for individual study with the active participation of students.
Assesment methods and criteria linked to learning outcomes
Course unit credit requirements: active participation in seminars, mastery of the subject matter, and the submission of a semestral assignment. Examination (written form): a practical part (5 tasks), a theoretical part (5 tasks); ECTS evaluation used.
Language of instruction
1. Fundamental mathematical concepts of risk engineering.
2. Selected deterministic models for economic and financial computations.
3. Selected deterministic models for numerical and engineering approaches, sensitivity analysis.
4. Uncertainty in risk engineering problems - stochastic and fuzzy models.
5. Problems of system reliability and risk evaluation modelling, simulation approaches.
6. Elementary models of decision making under parametric uncertainty.
7. Selected methods of estimating the probability distributions of model parameters. Statistical software.
8. Advanced mathematical statistics methods - linear and nonlinear multiple regression analysis.
9. Elements of categorical, factor and cluster analysis.
10. Parametric and nonparametric statistical hypothesis tests.
11. Models for dynamic problems - introduction to Markov chains (applications in production systems).
12. Elements of time series analysis.
13. Basic models for the quality control of production processes and products.
Students will gain useful knowledge of mathematical models used in risk modelling. They will also learn how to apply the studied models and methods to technical phenomena and processes.
Specification of controlled education, way of implementation and compensation for absences
Attendance at seminars is monitored, and the teacher decides on the manner of compensation for absences.