Στοχαστικές μέθοδοι πολυμεταβλητής μοντελοποίησης αποθεμάτων ασφαλιστικών χαρτοφυλακίων ζημιών

Abstract

The purpose of this paper is to examine the use of the Loss Reserving Methods and especially the use of a Multivariate version of the Chain – Ladder Method in the insurance companies. The aim is to introduce the readers the method in a simple and intuitive way. Based on Solvency II each insurance company is obliged to count and keep a capital adequacy for the possible claims that the insured clients will demand. Hence, it is very important for the company to count the reserves that must keep so as being solvent. The Multivariate Chain – Ladder method is one of the Loss Reserving Methods that counts the reserves the company must have. The Multivariate Chain – Ladder Method is based on a stochastic model such as the Chain – Ladder. It is the multivariate version of Schnaus model and extends the univariate model of Mack. It is preferred when the insurance portfolio consists several subportfolios with a certain dependence structure and it resolves in a way the problem of non- additivity of the univariate chain – ladder method. The chain – ladder method is the most famous method and it is widely used from the actuaries. This method applies in a single run – off triangle and it is well – known that the chain ladder’s predictors for the non – observable (future) total claims of a total portfolio consisting of several subportfolios differ, from the sums of the chain – ladder predictors for the non – observable total claims of the subportfolio. Finally, in this paper I will describe the data that we need for using run – off triangle techniques. Moreover, I will introduce the concept behind the mathematical techniques and I will demonstrate how run – off triangles are constructed for both incremental and cumulative claims loss amounts.