Μέτρα χρεοκοπίας για στοχαστικές διαδικασίες πλεονάσματος σε διακριτό χρόνο
Ruin measures for stochastic surplus processes in discrete time
KeywordsΔιαχείριση κινδύνου ; Στοχαστικές διαδικασίες ; Στοχαστική διαδικασία πλεονάσματος ; Χρεοκοπία ; Συνάρτηση Gerber-Shiu ; Ανανεωτικές ανελίξεις
The regular operation of an insurance company depends mainly on securing sufficient reserves, which may cover possible obligations to third parties or unexpected losses. They are also known as surplus identifying ruin probabilitywhich inform us in time, whether its reserves are sufficient or not. The beginning was by the Swedish mathematician Ernst Filip Oskar Lundberg (1903) who was working on issues of collective risk theory and matters of reinsurance, introducing also the compound Poisson model. After that Cramer (1930) helped him and the two of them as a team managed to combine the theory of stochastic processes with the risk theory and created the already classic model which is known as the model of Cramer – Lundberg. These two scientists also, concerned with the study of numbers of losses, according to Poisson distribution. In the meantime, Sparre Andersen appeared, and managed to prove the renewal model of risk theory with the numbers of losses be described by a renewal process. Last but not least Gerber and Shiu are mentioned, the two scientists who proved the the expected discount function of penalty. which combines all measures of ruin such as surplus, deficit and time of bankruptcy.