KNOWLEDGE – International Journal Vol.43.5 1131 MTPL CLAIMS UNCERTAINTY IN THE CHAIN LADDER METHOD Kleida Haxhi Department of Mathematical Engineering, Faculty of Mathematics and Physics Engineering, Polytechnic University of Tirana, Albania, k.haxhi@fimif.edu.al Abstract: Technical reserves, especially claims reserves are an important issue in a non-life insurance company. Under Albanian law reporting is done every quarter as well as the company's financial statements. The value of technical reserves affects directly the company's technical result. There are several methods for estimations the technical claims reserves. Initially, most of these methods began as deterministic algorithms. Over time actuaries began developing and analyzing stochastic models that justify these algorithms. These stochastic models enable analysis and quantification of the uncertainty of forecasting responsibilities for outstanding claims. Some of the models used are: The Poisson model, the over-dispersed Poisson model, Gamma model, Negative binomial model, and the Log-normal model. Parametric models such Wright‘s model and Bootstrap are also used. General linear models constitute a flexible class of stochastic models and are available in the analysis of future payments. Chain ladder model developed by Mack is the more prevalent model. This model is based on the triangle of development of incurred or paid claims and it is free distribution and also it does not require additional information. Based on the model of Mack, there are also developed other models easily applicable. Different methods yield different results, often similar to each other, but also different between them. These results are influenced by the available data. From the application made, it reached the conclusion that the data are often uncertain. The technical claims reserves, as all technical reserves directly affecting profit loss statement, as well as the technical balance of the company, it is required as fair evaluation of them. Results of application of stochastic methods are highly dependent on the reliability and accuracy of data. The actuary seeing the progress and history of claims in a portfolio, the market where are developed claims payments over the years, the values of outstanding claims, claims in process court, which values estimates is more appropriate to establish technical reserves. Also the insurance company must hold sufficient assets to cover technical reserves. The value of assets covering technical provisions must at all times be not less than the gross amount of technical reserves. Stochastic methods of reserves estimation discussed in this paper serve to assess the technical provisions of outstanding claims, as well as forecast cash payment of claims in the coming years. Keywords: stochastic methods, chain ladder model, uncertainty of data. 1. CHAIN LADDER METHOD The chain-ladder technique uses cumulative data, and derives a set of `development factors' or `link ratios'. To a large extent, it is irrelevant whether incremental or cumulative data are used when considering claims reserving in a stochastic context, and it is easier for he explanations here to use incremental. In order to keep the exposition as straightforward as possible, and without loss of generality, we assume that the data consist of a triangle of incremental claims. This is the simplest shape of data that can be obtained, and it is often the case that data from early origin years are considered fully run-off or that other parts of the triangle are missing. Using a triangle avoids us having to introduce complicated notation to confront with all possible situations. Thus, we assume that we have the following set of incremental claims data: C ij : i=1,…,n; j=1,….,n-i+1 The suffix i refers to the row, and could indicate accident year or underwriting year. The suffix j refers to the column, and indicates the delay, assumed also to be measured in years or quarterlies. The cumulative claims are defined by:   ∑    The chain-ladder technique estimates the development factors as:     ∑     ∑     These are then applied to the latest cumulative claims in each row D i,n-i+1 to produce forecasts of future values of cumulative claims:                  k=n-i+3, n-i+4,…..,n