Στοχαστικές διαδικασίες πλεονάσματος με Μαρκοβιανή εξάρτηση
Stohastic surplus processes under Markovian dependence
Παναγιωτάκου, Μαρία - Χριστίνα Γ.
KeywordsΘεωρία κινδύνου ; Στοχαστικές διαδικασίες ; Χαρτοφυλάκια ; Συναρτήσεις ; Χρεοκοπία ; Μαρκοβιανές διαδικασίες
Observing the occurrences of losses and corresponding indemnities to an insurance company, it is clear that developments in the economic and political environment, even weather variations, play an important role, since they affect the above figures to a large extent. The purpose of this paper is to study stochastic surplus processes in risk portfolios in a Markov environment. In particular, we will see how the stochastic processes better reflect reality in relation to the classic model of Risk Theory. In addition, we will refer in particular to certain risk measures such as the probability of bankruptcy and the probability of non-bankruptcy or survival, the deficit at the time of and before the bankruptcy, as well as relations linking these sizes through the Gerber-Shiu function. Finally, the expected dividends and their expected present value will be studied when there is a fixed dividend strategy.