Μελέτη τροποποιημένων ανανεωτικών στοχαστικών διαδικασιών πλεονάσματος στη θεωρία κινδύνου
Study of modified renewal stochastic surplus processes in risk theory
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Abstract
In risk theory, the analysis of quantities such as the deficit at ruin, the time of ruin, the surplus
immediately prior to ruin and the ruin probability is very important. The main focus of this
thesis is to study the abovementioned quantitates through the delayed renewal risk model
and the Gerber-Shiu function. Thus, in the first chapter, some background is introduced
regarding the ruin theory and the modified renewal risk processes.
In the second chapter, two important equations that are used as framework for the rest of
the thesis are derived. The first equation is obtained by conditioning on the first drop below
the initial surplus level, and the second one by conditioning on the amount and the time of
the first claim. Then, in chapter 3, we consider the deficit at ruin with the general delayed
model and some main results are given.
Lastly, in chapters 4 and 5, we explore how the Gerber-Shiu expected discounted penalty
function can be expressed in closed forms when distributional assumptions are given for claim
sizes or the time until the first claim.
Postgraduate Studies Programme
Αναλογιστική Επιστήμη και Διοικητική ΚινδύνουDepartment
Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής ΕπιστήμηςNumber of pages
76Language
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