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Lecturer(s)
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Linda Bohdan, doc. RNDr. CSc.
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Gogola Ján, RNDr. Ph.D.
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Course content
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Random process, its characteristics, classification of stochastic processes, insurance claims as a function of time, trend, stationarity. Random point processes - concept, the counting process of insurance claims, process intensity, aggregate insurance claims. Poisson processes homogeneous and nonhomogeneous, modeling of the incoming flow of insurance claims by a Polya process. Renewal processes, compound renewal processes, agragate insurance claims, ruin probability. Actuarial analysis of risks, risk reserve, Cramer-Lundberg approximation, profit realization, setting the premium. Markov chains, the Markov property, the matrix of transition probabilities, Chapman-Kolmogorov equations. Bonus-Malus system in auto-insurance.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Methods of individual activities
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Learning outcomes
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The aim of the course is to teach the students principles of stochastic processes for further use in the insurance system in practicing actuarial calculations, setting premium insurance and evaluating insured risks.
Capability of basic actuarial calculations, setting premium insurance and evaluating insured risks.
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Prerequisites
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Knowledge of probability and statistics.
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Assessment methods and criteria
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Home assignment evaluation, Student performance assessment, Work-related product analysis
Assignment - a written test (minimal requirement is 51% of all points), active attendance at seminars, completion of all given tasks.
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Recommended literature
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Stochastic modeling: Theory and reality from an actuarial perspective.. Ottawa: Association Actuarielle Internationale, 2010.
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Beichelt, Frank. Stochastic processes in science, engineering and finance. Boca Raton: Chapman & Hall CRC, 2006. ISBN 1-58488-493-2.
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BOLAND, P. J.:. Statistical and Probabilistic Methods in Actuarial Science.. Chapman, Boca Raton, FL, 2006.
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CIPRA, T.:. Finanční a pojistné vzorce.. Praha: GRADA Publishing., 2006.
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CIPRA, T. Pojistná matematika, teorie a praxe. Praha: EKOPRESS, 2006.
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Cipra, Tomáš. Finanční ekonometrie. Praha: Ekopress, 2008. ISBN 978-80-86929-43-9.
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DICKSON, D. C. M. Insurance Risk and Ruin.. Cambridge: Cambridge University Press., 2005.
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PACÁKOVÁ, V. Aplikovaná poistná štatistika. Bratislava: IURA EDITION, 2004.
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Rolski T. et al. Stochastic Processes for Insurance and Finance. Wiley, 2001.
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