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Stochastic Analysis in Financial Mathematics - NMFM535

Title:	Stochastická analýza ve finanční matematice
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2014 to 2015
Semester:	winter
E-Credits:	5
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	Mgr. Karel Janeček, Ph.D.
Class:	M Mgr. PMSE M Mgr. PMSE > Povinně volitelné
Classification:	Mathematics > Financial and Insurance Math.
Incompatibility :	NSTP175
Pre-requisite :	NMSA405
Interchangeability :	NSTP175
Is interchangeable with:	NSTP175, NSTP075

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KPMS (14.05.2013)

Black-Scholes model. Pricing of Options. The first and second fundamental theorems of mathematical finannce: The existence and uniqueness of the risk-neutral measure in relation to the existence of arbitrage and completness of the financial market. The Feynman-Kac theorem. Optimal Control - the problem of expected utility maximization. HJB equation approach (dynamic programming). Duality approach.

Aim of the course -

Last update: T_KPMS (14.05.2013)

The goal of the course is to explain modeling of stock prices, option

pricing, and optimal control. In the first part of the semester we

analyze models in disrete time -- the binomial model for the stock

price. In the second part we model the stock price by assuming the

geometric Brownian motion.

Literature - Czech

Last update: T_KPMS (14.05.2013)

Steven E. Shreve, Stochastic Calculus for Finance I

Steven E. Shreve, Stochastic Calculus for Finance II

Teaching methods -

Last update: T_KPMS (14.05.2013)

Lecture + exercises.

Syllabus -

Last update: T_KPMS (14.05.2013)

Black-Scholes model. Pricing of Options.

Optimal Control - the problem of expected utility maximization.

The first and second fundamental theorems of mathematical finance.