Στοχαστικές διατάξεις, θεωρία και εφαρμογές στο συλλογικό πρότυπο της θεωρίας κινδύνου
Stochastic orders: theory and applications in the collective risk model
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Keywords
Στοχαστικές διατάξεις ; Διαχείριση κινδύνου ; Κατανομές απώλειας ; Συλλογικό πρότυπο θεωρίας κινδύνουAbstract
The theory of stochastic orders is a useful tool in several fields of science such as statistics, finance, actuarial mathematics, epidemiology and other sciences. The theory of stochastic orders is the basis for approaching problems in actuarial science and insurance mathematics. The risk may come from a natural event (earthquake, fire, extreme weather, etc.), or from a human factor (negligence, accident, illness, etc.), or from economic activity. In actuarial science, the concept of risk is intertwined not with the nature and origin of the risk but with its economic consequences. Therefore, in actuarial science it is very useful to study the extent and magnitude of financial losses. The provision for financial losses can be made individually between two different potential losses or more broadly for entire portfolios. Comparing the risk between random situations as well as selecting the most appropriate risk measure can be done by applying the stochastic theory. The purpose of writing this dissertation is to approach the theoretical and practical application of stochastic orders in understanding and resolving issues related to actuarial science and risk management, with particular emphasis on the collective risk model. In the first chapter, an analysis of the basic theory of the usual stochastic orders is made. The second chapter presents useful applications of the stochastic theory developed in the first chapter using some particular examples of loss distributions. The third chapter approaches theory and applications that link individual risks and the collective risk model to the stop loss stochastic order. The fourth chapter, in the same way as the third chapter, approaches theory and applications that link individual risks and the collective risk model to the mean residual time stochastic order.
Postgraduate Studies Programme
Αναλογιστική Επιστήμη και Διοικητική ΚινδύνουDepartment
Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής ΕπιστήμηςNumber of pages
177Language
GreekCollections
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Attribution-NonCommercial-NoDerivatives 4.0 Διεθνές
Attribution-NonCommercial-NoDerivatives 4.0 Διεθνές