There are no prerequisites.

# Actuarial mathematics

Matej Kolar, Prof. Dr. Ermanno Pitacco

Mathematical models for insurance:

loss distribution,

methods to compute aggregate payments,

modeling of the claim frequencies,

recursive methods for aggregate loss computation,

credibility theory,

probability of default,

dependent risks modeling,

extreme events modeling,

stability.

H. H. Panjer, G. E. Willmot: Insurance Risk Models, Schaumburg, Society of Actuaries, 1992.

R. Kaas, M. Goovaerts, J. Dhaene, M Denuit: Modern Actuarial Risk Theory, Boston, Kluwer, 2001.

M. Denuit, J. Dhaene, M. Goovaerts, R. Kaas: Dependent Risks, Measures, Orders and Models, Wiley, 2005.

S. A. Klugman, H. H. Panjer, G. E. Willmot: Loss Models : From Data to Decisions, Wiley, 1998.

H. Bühlmann: Mathematical Methods in Risk Theory, Springer, 2005.

P. Embrechts, C. Klüppelberg, T. Mikosch: Modelling Extremal Events for Insurance and Finance, Springer, 1997.

The complexity of the insurance products requires more and more sofisticated mathematical models and more refined measures of risk. The course will cover current mathematical modelling for insurance.

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 risks and its measuring is a central issue in pricing and development of modern insurance products. Knowledge of the basic stochastic models for insurance is needed to assess the risks involved.

Application: The knowledge is directly applicable in insurance sector of the economy.

Reflection: Interplay between applications, statistical modelling and feedback information from other fields. Mathematical thinking based on concrete applications.

Transferable skills: Skills are transferable to many other fields of mathematical modelling. The value of the course is in concrete applications to insurance.

Lectures, exercises, homeworks, consultations

2 midterm exams instead of written exam, written exam

Oral exam

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

Mihael Perman:

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]

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]

Janez Bernik:

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, 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]

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]