M8F10 Mathematics and Statistical Methods in Insurance

Faculty of Science
Spring 2025
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martin Kolář, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Mastering the basics of financial and actuarial mathematics.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Students will be informed of the possibility of using mathematical and statistical methods in insurance activities of commercial insurance companies operating in the insurance market in the Czech Republic.
Learning outcomes
After completing this course, students will be able to understand the basic principles of calculation of premiums and making insurance reserves.
Syllabus
  • Probability distributions and their characteristics in actuarial mathematics, Tails of distributions and their classification, risk measures, TVaR Continuous models, operations with distributions Division of class (a, b, 0) and (a, b, 1) Compound counting distributions, Panjer's recursion Reading processes Processes with independent increments, operating time Reading Markov processes with positive and negative infection Recovery processes Mixed Poisson processes Zero modification and truncation Total loss models Compound Poisson process Methods for calculating the total demand, analytical, recursive and inverse methods Ruin theory Adjustment coefficient and Lundberg inequality Cramer's asymptotic formula
Literature
    required literature
  • CIPRA, Tomáš. Pojistná matematika : teorie a praxe. Vyd. 1. Praha: Ekopress, 1999, 398 s. ISBN 8086119173. info
  • CIPRA, Tomáš. Finanční a pojistné vzorce. 1. vyd. Praha: Grada, 2006, 374 s. ISBN 802471633X. info
  • CIPRA, Tomáš. Zajištění a přenos rizik v pojišťovnictví. 1. vyd. Praha: Grada, 2004, 260 s. ISBN 8024708388. info
  • ŘEZÁČ, František, Gabriela OŠKRDALOVÁ, Martin ŘEZÁČ, Miroslava ŠIKULOVÁ and Petr VALOUCH. Marketingové řízení komerční pojišťovny (Marketing management of insurace company). 1. vyd. Brno: Masarykova univerzita, Tisk: BonnyPress, 2009, 210 pp. ISBN 978-80-210-4799-0. info
    not specified
  • KLUGMAN, Stuart A., Harry H. PANJER and Gordon E. WILLMOT. Loss models : from data to decisions. 4th ed. Hoboken, N.J.: John Wiley & Sons, 2012, xiv,511 s. ISBN 9781118315323. info
Teaching methods
Lectures, homeworks
Assessment methods
Successful completion of this course is at least 60% success rate in the written examination.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2012, spring 2012 - acreditation, Spring 2014, Spring 2016, spring 2018, Spring 2021, Spring 2023.
  • Enrolment Statistics (recent)
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