Στοχαστικά μοντέλα στη θεωρία κινδύνου με εξάρτηση και διάχυση
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Keywords
Θεωρία χρεοκοπίας ; Δομή εξάρτησης ; Στοχαστικά μοντέλαAbstract
In ruin theory, for many years, it was a common practice for modeling the stochastic process of surplus to use the Cramer-Lundberg model (classic model) or the renewal model (Sparre-Andersen model). For the aforementioned, it was necessary the independence hypothesis between the amount of the claims and the intermediate times of two successively claims. The reality is different, so in recent years the research has focused in finding and developing models with dependence structure. In this thesis, we will focus in a model, whose distribution of time until the next claim depends on the amount of the previous claim, more specifically the distribution of the intermediate time between two successively claims depends on the amount of the claim that precedes in time. In the first two chapters, basic results of the stochastic process theory, ruin theory and necessary information for the following chapters are presented. In the third chapter, a model with a dependence structure is presented. We analyze the generalized Lundbergs’ equation, the Gerber-Shiu function, and the important results such as the Laplace transform of the time at ruin, examples are given in order to illustrate this structure. In the fourth chapter in the model with the dependence structure with add a diffusion factor and we focus on the Lundbergs’ equation, the Gerber-Shiu function (in order to extract ruin measures such as the probability of ruin or the surplus at the exact time before the ruin) and some integrodifferential equations for this specific model. In the fifth chapter , a dual model with a dependence structure is introduced and analyzed. Further discussion for the Laplace transform of the time at ruin is given.
Postgraduate Studies Programme
Αναλογιστική Επιστήμη και Διοικητική ΚινδύνουDepartment
Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής ΕπιστήμηςNumber of pages
68Language
GreekCollections
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Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα
Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα