SubjectsSubjects(version: 953)
Course, academic year 2023/2024
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Probability for Finance and Insurance - NMFP405
Title: Pravděpodobnost pro finance a pojišťovnictví
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022 to 2023
Semester: winter
E-Credits: 4
Hours per week, examination: winter s.:2/1, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: prof. RNDr. Bohdan Maslowski, DrSc.
Class: M Mgr. FPM
M Mgr. FPM > Povinné
Classification: Mathematics > Financial and Insurance Math.
Incompatibility : NMFM408
Interchangeability : NMFM408
Is incompatible with: NMFM408
Is pre-requisite for: NMFM507
Is interchangeable with: NMFM408
In complex pre-requisite: NMFP505, NMTP533, NMTP543
Annotation -
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.
Last update: Branda Martin, doc. RNDr., Ph.D. (14.12.2020)
Aim of the course -

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

Last update: Zichová Jitka, RNDr., Dr. (01.06.2022)
Course completion requirements -

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.

Last update: Maslowski Bohdan, prof. RNDr., DrSc. (28.09.2023)
Literature -

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

Last update: Maslowski Bohdan, prof. RNDr., DrSc. (14.12.2020)
Teaching methods -

Lecture + exercises.

Last update: Zichová Jitka, RNDr., Dr. (01.06.2022)
Syllabus -

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.

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