Subjects

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Stochastic Models in Finance 2 - NMFP534

Title:	Stochastické modely ve financích 2
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
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:	English, Czech
Teaching methods:	full-time

Guarantor:	doc. RNDr. Jan Večeř, Ph.D.
Teacher(s):	doc. RNDr. Jan Večeř, Ph.D.
Class:	M Mgr. FPM M Mgr. FPM > Povinně volitelné M Mgr. PMSE M Mgr. PMSE > Volitelné
Classification:	Mathematics > Financial and Insurance Math.

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Annotation -

This course covers more advanced topics of finance in continuous time. It covers optimal behavior of market agents who maximize their utility functions, its implications to optimal portfolio selection, connections to stochastic optimal control. The course also covers pricing exotic option contracts and considers evolution of the asset price driven by jump processes.

Last update: Branda Martin, doc. RNDr., Ph.D. (19.12.2020)

Literature -

Vecer, J.: Stochastic Finance, CRC Press, 2011.

Merton, R.: Continuous Time Finance, Blackwell 1999.

Karatzas, I., Shreve, S.: Methods of Mathematical Finance, Springer 2017.

Last update: Branda Martin, doc. RNDr., Ph.D. (19.12.2020)

Teaching methods -

Lecture.

Last update: Zichová Jitka, RNDr., Dr. (13.05.2023)

Syllabus -

Optimal control - the problem of maximizing the mean value of the utility function.

Merton's optimal portfolio and its generalization to the optimal behavior of an agent with a different distribution view than market.

Complex financial contracts, lookback options, drawdown options, Asian options, their valuation and hedging.

Non-diffusion price evolution, Poisson process, price models with infinite jump intensity.

Last update: Branda Martin, doc. RNDr., Ph.D. (19.12.2020)