Topics in financial mathematics 1

There are no prerequisites.

Lecturer can choose amon the following and some other current topics in financial mathematics:
Credit risk models: basic definitions, basic models, pricing of credit derivatives.
Risk management: risk measures, coherence, dynamic risk measures, copula models, extreme value theory, optimal strategies, risk management models.

M. Ammann: Credit Risk Valuation : Methods, Models and Applications, 2nd edition, Springer, Berlin, 2001.
J. Grandell: Aspects of Risk Theory, Springer, New York, 1992.
I. Karatzas, S. E. Shreve: Methods of Mathematical Finance, Springer, New York, 2001.
T. Björk: Arbitrage Theory in Continuous Time, 2nd edition, Oxford Univ. Press, Oxford, 2004.
P. Wilmott: Derivatives : The Theory and Practice of Financial Engineering, Wiley, New York, 2000.
A. J.McNeil, R. Frey, P. Embrechts, Paul: Quantitative risk management: Concepts, techniques and tools, Princeton Series in Finance, Princeton University Press, Princeton, NJ, 2005.
P. Embrechts, C. Klüppelberg, T. Mikosch: Modelling extremal events for insurance and finance, Springer-Verlag, Berlin, 1997.

The course covers topics im mathematical finance in which economic reasoning is combined with advanced mathematical tools.
Some of them are based on previous courses and give additional interpretation, some contribute to understanding of the risks.
Since the content is of great practical importance we expect that also specialists from financial practice will present their work experience during the course.

Knowledge and understanding:
Understanding of mathematical models used in mathematical finance and the mathematical tools used in solutions.
Application:
The knowledge and skills acquired are directly transferable and can also serve for combining mathematical reasoning with economic topics.
Reflection:
The subject of the course, hence the course itself, combines numerous mathematical skills starting from linear algebra to partial differential equations.
Transferable skills:
The knowledge and skills acquired are immediately applicable in financial institutions such as banks and insurance companies. The content alsoserves to deepen the ability to use mathematical models.

Lectures, exercises, consultations, seminars

Individual seminar
Completed seminar work is required for the exam on the course content
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Tomaž Košir:
BERNIK, Janez, DRNOVŠEK, Roman, KOKOL-BUKOVŠEK, Damjana, KOŠIR, Tomaž, OMLADIČ, Matjaž, RADJAVI, Heydar. On semitransitive jordan algebras of matrices. Journal of algebra and its applications, ISSN 0219-4988, 2011, vol. 10, iss. 2, str. 319-333. [COBISS-SI-ID 15908697]
KOŠIR, Tomaž, OBLAK, Polona. On pairs of commuting nilpotent matrices. Transformation groups, ISSN 1083-4362, 2009, vol. 14, no. 1, str. 175-182. [COBISS-SI-ID 15077977]
BERNIK, Janez, DRNOVŠEK, Roman, KOŠIR, Tomaž, LIVSHITS, Leo, MASTNAK, Mitja, OMLADIČ, Matjaž, RADJAVI, Heydar. Approximate permutability of traces on semigroups of matrices. Operators and matrices, ISSN 1846-3886, 2007, vol. 1, no. 4, str. 455-467. [COBISS-SI-ID 14492761]