Ανάλυση των αναμενόμενων προεξοφλημένων συναρτήσεων ποινής των Gerber-Shiu για το ανανεωτικό μοντέλο της θεωρίας κινδύνου
Analysis of the expected discounted penalty functions of Gerber-Shiu for the renewal model of risk theory
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Keywords
Συνάρτηση ποινής ; Gerber - Shiu ; Θεωρία κινδύνουAbstract
In an insurance organization, where the services it provides are the coverage against risks, there are two aspects that make up the concept of insurance coverage. One side concerns the organization's revenue, i.e., insurance premiums, while the other concerns expenses, i.e., the provision of compensation. For the smooth operation of the organization, the revenue should be sufficient to cover the costs, because the opposite means a breach of the agency's obligations, i.e., inability to provide compensation. Actuarial science deals with the study of these quantities and in this thesis, we deal with a subject that is one of the most important in this science. The issue is the so-called "ruin", that is, the default of obligations by the insurance organization. The study done in this paper concerns the presentation of a very useful mathematical tool and the way we can use it to get valuable information about quantities that are related to ruin. It is a mathematical function that has several parameters that make it so valuable as we can derive a wealth of information for specific choices of individual parameters that help us to understand as best as possible the event of ruin. This function is called the "Gerber – Shiu function" and was named after Hans U. Gerber and Elias S. W. Shiu, who presented this valuable tool in "The North American Actuarial Journal" in January 1998 entitled "On the time value of ruin". In this work we present necessary knowledge required to understand this tool, some cases for specific parameters as well as the generalization of the function.