Topics in financial mathematics

There are no prerequisites.

The content consists of a selection of standard topics in advanced financial mathematics. Possible chapters are:

-Stochastic integration.
-Stochastic differential equations.
-Valuation of options.
-Stochastic optimal control.
-Optimal stopping and American options.
The choice depends on students' research interests.

1. T. Björk: Arbitrage theory in continuous time, 2nd ed., Oxford : Oxford University Press, 2004.
2. I. Karatzas, S. E. Shreve: Methods of mathematical finance, 2nd ed., New York : Springer, cop. 1998.
3. I. Karatzas, S. E. Shreve: Brownian motion and stochastic calculus, 2nd ed., New York : Springer, cop. 1998.
4. D. Revuz, M. Yor: Continuous martingales and Brownian motion, Berlin : Springer, 1991.

The main goal of the course is to provide students with some important topics in financial mathematics.

Knowledge and comprehension of presented concepts.
Ability to use acquired knowledge and skills.

Lectures, consultations, problem sessions

Written exam (homeworks), oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

BERNIK, Janez, MASTNAK, Mitja, RADJAVI, Heydar. Realizing irreducible semigroups and real algebras of compact operators. Journal of mathematical analysis and applications, ISSN 0022-247X. [Print ed.], 2008, vol. 348, no. 2, str. 692-707. [COBISS-SI-ID 14899289]
BERNIK, Janez, MARCOUX, Laurent W., RADJAVI, Heydar. Spectral conditions and band reducibility of operators. Journal of the London Mathematical Society, ISSN 0024-6107, 2012, vol. 86, no. 1, str. 214-234. [COBISS-SI-ID 16357721]
BERNIK, Janez, MASTNAK, Mitja. Lie algebras acting semitransitively. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 2013, vol. 438, iss. 6, str. 2777-2792. [COBISS-SI-ID 16553561]
PERMAN, Mihael. An excursion approach to Ray-Knight theorems for perturbed Brownian motion. Stochastic Processes and their Applications, ISSN 0304-4149. [Print ed.], 1996, let. 63, str. 67-74. [COBISS-SI-ID 7621465]
PERMAN, Mihael, WELLNER, Jon A. On the distribution of Brownian areas. Annals of applied probability, ISSN 1050-5164, 1996, let. 6, št. 4, str. 1091-1111. [COBISS-SI-ID 7101017]
PERMAN, Mihael, WELLNER, Jon A. An excursion approach to maxima of the Brownian bridge. Stochastic Processes and their Applications, ISSN 0304-4149. [Print ed.], 2014, vol. 124, iss. 9, str. 3106-3120. [COBISS-SI-ID 17154393]