Course detail
Mathematical Foundations of Risk Analysis
ÚSI-2SAMZAcad. year: 2015/2016
The course is based on mathematical modelling and its applications in risk engineering. The explanation is oriented on explication of fundamental ideas and notions, especially by means of suitable examples, on their applicability and on unifying view of mathematical principles. Related mathematical methods of solutions for individual areas will be presented with the use of suitable the software: Statistics, Minitab, Mat lab, and Excel.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
2. Selected deterministic models for economic and financial computations.
3. Selected deterministic models for numerical and engineering approaches, sensitivity analysis.
4. Uncertainty in problems of risk engineering - stochastic and fuzzy models.
5. Problems of systems reliability and risks evaluations modelling, simulation approach.
6. Elementary models of decision making under uncertainty.
7. Selected estimation methods of models parameters probability distributions. 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 hypotheses tests.
11. Models for dynamic problems - introduction to Markov chains (applications in production systems).
12. Elements of time series analysis.
13. Basic models for quality control of production and produces.
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
CIPRA, T.: Finanční matematika, MatFyzPress, 1993, ISBN 80-901495-1-0
CIPRA, T: Modely časových řad, SNTL, 1998.
HNILICA, J., FOTR, J.: Aplikovaná analýza rizika ve finančním managementu a investičním rozhodování. Praha : Grada, 2009, ISBN 978-80-247-2560-4.
KLAPKA A KOL.: Metody operačního výzkumu, VUTIUM 2001, ISBN 80-214-1839-7
Recommended reading
MONTGOMERY, D. C., RENGER, G.: Applied Statistics and Probability for Engineers. New York : John Wiley & Sons, 2003.
WILLIAMS, H. P.: Model Building in Mathematical Programming, Wiley 1993, ISBN 0471941115.
Classification of course in study plans
- Programme MRzI Master's
branch RSZ , 1 year of study, winter semester, compulsory
branch REZ , 1 year of study, winter semester, compulsory
branch RIS , 1 year of study, winter semester, compulsory
branch RCH , 1 year of study, winter semester, compulsory
branch RFI , 1 year of study, winter semester, compulsory
branch RSK , 1 year of study, winter semester, compulsory