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
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 -
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.

Course completion requirements -
Last update: doc. RNDr. Jan Večeř, Ph.D. (06.03.2018)

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

Requirements to the exam -
Last update: doc. RNDr. Jan Večeř, Ph.D. (06.03.2018)

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

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

A calculus based course on probability.