Subjects

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Probability for Financial Mathematics - NMFM202

Title:	Pravděpodobnost pro finanční matematiky
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2024
Semester:	summer
E-Credits:	8
Hours per week, examination:	summer s.:4/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time

Guarantor:	RNDr. Jitka Zichová, Dr.
Teacher(s):	Mgr. Martin Romaňák RNDr. Jan Vávra, Ph.D. RNDr. Jitka Zichová, Dr.
Class:	M Bc. FM M Bc. FM > Povinné M Bc. FM > 2. ročník
Classification:	Mathematics > Probability and Statistics
Pre-requisite :	{One course in Linear Algebra}, NMMA221
Is co-requisite for:	NMFM201
Is pre-requisite for:	NMFM311, NMFM301
Is interchangeable with:	NSTP129

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Annotation -

Introductory course in probability theory for program in Financial mathematics. Elementary and axiomatic definition of probability. Random events and their probability. Random variables and their probability distributions. Random vectors. Converegence of random variables and vectors.

Last update: Zichová Jitka, RNDr., Dr. (21.05.2021)

Aim of the course -

To explain foundations of probability theory.

Last update: G_M (15.05.2012)

Course completion requirements -

The subject is finalized by tutorial credit and exam.

Tutorial credit requirements:

active presence at the exercises, completing two written tests (at least 50% of points).

For each test one additional attempt.

Last update: Zichová Jitka, RNDr., Dr. (23.05.2025)

Literature - Czech

Základní:

Michal Kulich: Základy teorie pravděpodobnosti pro předmět Matematická statistika 1. KPMS MFF UK, 2018. Dostupné na http://www.karlin.mff.cuni.cz/~zichova/.

Karel Zvára, Josef Štěpán: Pravděpodobnost a matematická statistika. Matfyzpress, Praha 2002.

Václav Dupač, Marie Hušková: Pravděpodobnost a matematická statistika. Karolinum, Praha, 1999.

Jiří Anděl: Základy matematické statistiky. Matfyzpress, Praha 2005.

Doplňková:

Jiří Anděl: Matematická statistika. SNTL, Praha, 1985.

R.C. Rao: Lineární metody statistické indukce a jejich aplikace. Academia, Praha, 1978.

Alfred Rényi: Teorie pravděpodobnosti. Academia, Praha, 1972.

Josef Štěpán: Teorie pravděpodobnosti. Matematické základy. Academia, Praha, 1987.

Last update: Zichová Jitka, RNDr., Dr. (23.05.2019)

Teaching methods -

Lecture+exercises.

Last update: G_M (24.04.2012)

Requirements to the exam -

Written exam corresponding to the syllabus.

Last update: Zichová Jitka, RNDr., Dr. (20.05.2025)

Syllabus -

Elementary and axiomatic definition of probability.

Random events and their probability.

Random variables and their probability distributions.

Random vectors. Conditional distributions. Transformatins.

Converegence of random variables and vectors.

Last update: Zichová Jitka, RNDr., Dr. (19.04.2018)

Entry requirements -

Basics of calculus, measure theory and linear algebra.

Last update: Zichová Jitka, RNDr., Dr. (20.05.2025)