Η κλάση κατανομών (a,b,0) του Panjer: θεωρία, γενικεύσεις και εφαρμογές στη θεωρία συλλογικού κινδύνου
The Panjer (a,b,0) class of distributions: theory, generalizations and applications in collective risk theory
A significant quantity in risk theory is the total amount of compensation for a given portfolio, which depends on the number and the amount of the claims. In this dissertation we study the cases where the number of claims belongs to some of the classes of distributions R(a,b,0), R(a,b,1) and R(a,b,l). In particular, for the class of distributions R(a,b,0) we study an article by Fackler (2009), in which the probability function of the number of claims is given with a non-recursive formula. For these cases, both recursive and non-recursive formulas of calculation of the total amount of compensation are given when the amount of individual claims follows either a continuous or a discrete distribution. In addition, we analyze the methods of discretization a continuous random variable using the programming language R. Finally, some numerical examples are given for calculating the probability functions of the total amount of compensation using the programming language R.