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 2023
Semester: summer
E-Credits: 5
Hours per week, examination: summer 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: English, Czech
Teaching methods: full-time
Is provided by: NMFM505
Guarantor: doc. RNDr. Jan Večeř, Ph.D.
Class: M Mgr. PMSE
M Mgr. PMSE > Povinně volitelné
Classification: Mathematics > Financial and Insurance Math.
Pre-requisite : {One course of advanced Theory of Probability}
Incompatibility : NMFM505
Interchangeability : NMFM505
Is incompatible with: NMFM505
Is interchangeable with: NMFM505, NSTP075, NSTP175
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Annotation -
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.
Last update: T_KPMS (14.05.2013)
Aim of the course -

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.

Last update: T_KPMS (14.05.2013)
Course completion requirements -

Class attendance during the semester, the last class being mandatory.

Last update: Večeř Jan, doc. RNDr., Ph.D. (06.03.2018)
Literature - Czech

Steven E. Shreve, Stochastic Calculus for Finance I

Steven E. Shreve, Stochastic Calculus for Finance II

Last update: T_KPMS (14.05.2013)
Teaching methods -

Lecture + exercises.

Last update: T_KPMS (14.05.2013)
Requirements to the exam -

A written final exam covering the topics listed in the syllabus.

Last update: Večeř Jan, doc. RNDr., Ph.D. (06.03.2018)
Syllabus -

Black-Scholes model. Pricing of Options.

Optimal Control - the problem of expected utility maximization.

The first and second fundamental theorems of mathematical finance.

Last update: T_KPMS (14.05.2013)
Entry requirements -

A calculus based course on probability.

Last update: Zichová Jitka, RNDr., Dr. (17.06.2019)