Subjects(version: 942)
Course, academic year 2023/2024
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Probability for Finance and Insurance - NMFP405
Title: Pravděpodobnost pro finance a pojišťovnictví Department of Probability and Mathematical Statistics (32-KPMS) Faculty of Mathematics and Physics from 2022 winter 4 winter s.:2/1, C+Ex [HT] unlimited unlimited no no taught English, Czech full-time full-time
Guarantor: prof. RNDr. Bohdan Maslowski, DrSc. M Mgr. FPMM Mgr. FPM > Povinné Mathematics > Financial and Insurance Math. NMFM408 NMFM408 NMFM408 NMFM507 NMFM408 NMFP505, NMTP533, NMTP543
 Annotation - ---CzechEnglish
Last update: doc. RNDr. Martin Branda, Ph.D. (14.12.2020)
The main objective is to introduce the fundamentals of probability theory that are used in finance and insurance mathematics. The central concepts here are conditional expectation and discrete and continuous martingales that will be introduced and explained. Their basic properties will be studied and the most important examples (Wiener process and stochastic integral) will be examined. Basics of the stochastic calculus will be introduced and studied (Ito Lemma). These techniques form the fundamentals for investigation of stochastic models in finance and insurance mathematics.
 Aim of the course - ---CzechEnglish
Last update: RNDr. Jitka Zichová, Dr. (01.06.2022)

The main objective is to introduce the fundamentals of probability theory that are used in finance and insurance mathematics.

 Course completion requirements - ---CzechEnglish
Last update: prof. RNDr. Bohdan Maslowski, DrSc. (28.09.2023)

The credit for exercise class must be obtained prior to taking the exam.

The credit for exercise class is obtained for personal presence at four (at least) exercise classes (the total number of which is seven). If this condition is not met, it is necessary to submit solutions to assigned exercise in written form.

 Literature - ---CzechEnglish
Last update: prof. RNDr. Bohdan Maslowski, DrSc. (14.12.2020)

P. Lachout: Diskrétní martingaly, Lecture Notes MFF UK

B. Oksendal: Stochastic Differential Equations, Springer-Verlag, 2010

I. Karatzas and S.E. Shreve: Brownian Motion and Stochastic Calculus, Springer-Verlag, 1988

J. M. Steele, Stochastic Calculus and Financial Applications, Springer-Verlag, 2001

 Teaching methods - ---CzechEnglish
Last update: RNDr. Jitka Zichová, Dr. (01.06.2022)

Lecture + exercises.

 Syllabus - ---CzechEnglish
Last update: prof. RNDr. Bohdan Maslowski, DrSc. (14.12.2020)

1. Conditional expectation w.r.t. sigma-algebra, random process, finite-dimensional distributions, Daniell-Kolmogorov and Kolmogorov-Chentsov theorems.

2. Martingales, definition of super- and submartingales, filtration, basic examples. Stopping times and hitting times of a subset of the state space by a random process. Maximal inequalities, Doob-Meyer decomposition.

3. Quadratic variation of martingales, Wiener process and its basic properties.

4. Stochastic integration w.r.t. Wiener process, definition and basic properties. Stochastic differential and Ito formula, examples.

5. Stochastic integration w.r.t. martingales - an introduction.

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