Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

Probability for Finance and Insurance - NMFM408

Title:	Pravděpodobnost pro finance a pojišťovnictví
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2013 to 2014
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, 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
Teaching methods:	full-time

Guarantor:	prof. RNDr. Bohdan Maslowski, DrSc.
Class:	M Mgr. FPM M Mgr. FPM > Povinné
Classification:	Mathematics > Probability and Statistics
Is pre-requisite for:	NMFM507, NMFM505
In complex pre-requisite:	NMST531

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KPMS (01.06.2016)

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 -

Last update: T_KPMS (17.05.2013)

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

mathematics.

Literature - Czech

Last update: T_KPMS (11.05.2015)

P. Lachout: Diskrétní martingaly, skripta MFF UK

B. Oksendal: Stochastic Differential Equations, Springer-Verlag, 2010 (sedmé vydání)

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

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

Teaching methods -

Last update: T_KPMS (17.05.2013)

Lecture.

Syllabus -

Last update: T_KPMS (11.05.2015)

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.