Στοχαστικές διαδικασίες κινδύνου με εξάρτηση μεταξύ των μεγεθών των ζημιών και των χρόνων εμφάνισης των κινδύνων
Stochastic risk processes with dependent individual claim sizes and inter-claim times
In this thesis, we focus on the study and presentation of Stochastic risk processes with dependent individual claim sizes and inter-claim times. For a century now study of risk theory, from the classical model of risk theory to more complex models that have appeared from time to time. In 1998, Gerber and Shiu proposes the known penalty function, and from then the study of risk theory is wandering around this function. The use of the copula, and general forms of dependence for bivariate variables is becoming popular in actuarial science and risk management, was not long until it came to risk theory. Some models are more realistic and represent the reality when a form of dependence between the amount of damage (regular or catastrophic) and the risk of time is used. First will be the presentation of risk theory and the Gerber-Shiu function, then we will analyze the generalized Gerber-Shiu function in a model with dependence between individual claim sizes and inter-claim times. We will introduce a general dependency class for the bivariate variable containing specific cases and with numerical examples the influence of dependence in the probability of default will be determined.