Completed course Operation research.

# Financial lab

Course consists of two parts.

The aim of the lectures and the seminar is to deepen the understanding of the material learned in Operations Research and Financial Mathematics 1 courses by presenting it in the theoretical framework acquired at the courses in probability and statistics (e.g., the theory of martingales in discrete time) and/or use the

knowledge acquired in the above courses to present stochastic modeling in finance and insurance (e.g. collective models, modeling the number of claims, modeling the size of claims, modeling of returns).

For the practical part students are given a couple of projects that they start to work on under supervision and finish themselves.

Some possible topics for projects with practical objectives:

Statistical project: data collection, data preparation, model selection, model testing,

parameter estimation, interpretation, forecasting, reliability testing, simulations, Monte Carlo methods, probit and logit models, regression models for analysis of financial data.

Finance project: practical evaluations of options, recursive methods, simulation methods, estimation of “greeks”, difference methods, single equity analysis, optimal investment strategies and numerical implementations, Monte Carlo methods, interest rate and currency derivatives.

Actuarial project: determining the premia of complex insurance products, probit and logit models for risk assessment, probability of ruin estimation, loss reserves estimation, long-term

risk estimation.

Each student is required to make a project related to Operations Research. The topics of the projects will be based on material from books or articles in specialized journals like for example European Journal of Operational Research, INFORMS Journal on Computing, Computers & Operations Research, etc.

P. Wilmott: Derivatives: The Theory and Practice of Financial Engineering, John Wiley & Sons, New York, 1998.

W.N. Venables, B. Ripley: S-programming, Springer, 2004.

D.A. Freedman: Statistical models, Theory and Practice, Cambridge Univ. Press. 2005.

H. P. Schmidli: Risk theory, script freely available on the internet, www.math.ku.dk/~schmidli/rt.pdf .

A. Klenke: Probability Theory, A Comprehensive Course, Springer-Verlag 2006.

V. Batagelj: Operacijske raziskave. Skripta v pripravi. http://vlado.fmf.uni-lj.si/vlado/or/or.htm

D. C. Montgomery: Design and analysis of experiments. John Wiley & Sons, 1997.

F.S. Hillier in G.J. Lieberman: Introduction to operations research. McGraw-Hill Higher Education, 2010.

W.L. Winston: Operation Research, Applications and Algorithms. PWS-KENT, Boston, MA 1991.

On the one hand the theoretical background of

concepts learned in Financial Mathematics 1 course are elucidated and skills acquired in Probability course are used in stochastic modeling in finance and insurance.

On the other, the concepts of financial mathematics and statistics only become apparent through practical experience. This is the goal of the practical part of this course. Students will prepare under tutorship projects in statistics or financial mathematics involving real-life data and computer programs.

Knowledge and understanding: Understanding of the theoretical concepts in probability, statistics and financial mathematics , and the ability to apply them to concrete real-life examples and data. Without adequate computer equipment these notions remain incomplete, and the skills needed for successful employment are not developed.

Application: The ability to implement in practice the concepts of financial mathematics is crucial for the skills development. The applications are straightforward.

Reflection:

The practical experience in valuation of financial products enables deeper understanding of the underlying theoretical concepts.

Transferable skills:

The skills obtained are transferable to all areas

of probability, stochastic processes and mathematical modelling, but most of all to real-life problems.

Lectures, seminar and projects under supervision

Quality of a submitted projects

Oral defense

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

Janez Bernik:

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]

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, RADJAVI, Heydar. Positivity and matrix semigroups. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 2011, vol. 434, iss. 3, str. 801-812. [COBISS-SI-ID 15745625]

Sergio Cabello:

CABELLO, Sergio, ROTE, Günter. Obnoxious centers in graphs. SIAM journal on discrete mathematics, ISSN 0895-4801, 2010, vol. 24, no. 4, str. 1713-1730. [COBISS-SI-ID 15762265]

BUCHIN, Kevin, CABELLO, Sergio, GUDMUNDSSON, Joachim, LÖFFLER, Maarten, LUO, Jun, ROTE, Günter, SILVEIRA, Rodrigo I., SPECKMANN, Bettina, WOLLE, Thomas. Finding the most relevant fragments in networks. Journal of graph algorithms and applications, ISSN 1526-1719, 2010, vol. 14, no. 2, str. 307-336. [COBISS-SI-ID 15629401]

CABELLO, Sergio, DÍAZ-BÁÑEZ, José Miguel, LANGERMAN, Stefan, SEARA, Carlos, VENTURA, Inma. Facility location problems in the plane based on reverse nearest neighbor queries. European journal of operational research, ISSN 0377-2217. [Print ed.], 2010, vol. 202, iss. 1, str. 99-106. [COBISS-SI-ID 15160921]

Mihael Perman:

KOMELJ, Janez, PERMAN, Mihael. Joint characteristic functions construction via copulas. Insurance. Mathematics & economics, ISSN 0167-6687, 2010, vol. 47, iss. 2, str. 137-143. [COBISS-SI-ID 16242777]

HUZAK, Miljenko, PERMAN, Mihael, ŠIKIĆ, Hrvoje, VONDRAČEK, Zoran. Ruin probabilities and decompositions for general perturbed risk processes. Annals of applied probability, ISSN 1050-5164, 2004, vol. 14, no. 3, str. 1378-1397. [COBISS-SI-ID 13168985]

HUZAK, Miljenko, PERMAN, Mihael, ŠIKIĆ, Hrvoje, VONDRAČEK, Zoran. Ruin probabilities for competing claim processes. Journal of Applied Probability, ISSN 0021-9002, 2004, vol. 41, no. 3, str. 679-690. [COBISS-SI-ID 13207641]