Μέτρα χρεοκοπίας : ανάλυση της κλασσικής και γενικευμένης συνάρτησης των Gerber - Shiu
Ruin measures : analysis of the classical and generalized Gerber - Shiu function
KeywordsΔιαχείριση κινδύνου ; Στοχαστικά μοντέλα ; Συναρτήσεις ; Στοχαστικές διαδικασίες ; Στατιστική ανάλυση ; Χρεοκοπία
If we are asked to give the definition of «ruin», we would probably answer that is the organization’s incapability of paying its liabilities. However from an Actuary’s point of view, we would say that is the case when the initial surplus becomes negative without this fact leading necessarily to the ruin of the organization but the insurance portfolio did not designed in the right way. Specifically, the role of Actuarial Science is that it has to study more deeply these measures of ruin which can bring terrible consequences and disasters to an organization. As we can observe though , the measure of ruin is a very useful and significant tool for the Actuarial Science. In particular, an organization for example an insurance company, when quantifies and models the measures which can be faced in a future ruin, the company is able to avoid them and save its economic stability and occurrence. In 1998, the team Gerber and Shiu , in their article named “On the time value of ruin”, revealed only one function which contains all these measures which are at the same time interesting and important for an insurance company ,namely the time of ruin ,the deficit at ruin and the surplus immediately prior to ruin. The name of this function is the Gerber – Shiu expected discounted penalty function or else known as Gerber – Shiu function in short. In this thesis, we will present the most important ruin measures and we will analyze them from the point of the classical and the general way of the Gerber – Shiu function. Then we will illustrate a variety of different models in order to analyze the surplus from a stochastically point of view.