VIDEO SCREEN EXPLANATION

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2 INTRODUCTION The Actuarial Laboratory (A.L.) is an interactive, user friendly and powerful software to produce easily and rapidly sophisticated statistical analysis concerning mass risk insurance. The first version concerns risk analysis and rating for Motor insurance. In general terms, the A.L. is structured in five steps: 1) descriptive risk analysis: At the beginning the user may need some simple information about the risk. This step allows him to evaluate observed values for the most important risk indexes (e.g. claim frequency, average cost, pure premium, premium rate, etc...). The user can evaluate them for each variable separately (univariate analysis) and for each couple of variables (bivariate analysis). 2) variable class grouping: Before proceeding with the analysis, it is certainly useful to group some variables into homogeneous groups in order to reduce the number of possible classes of risk and, consequently, to have more reliable premium estimations for each of them. 3) selection of variables (multivariate risk analysis): The tariff must be calculated using a small number of all the available variables; consequently, it is crucial to choose the most important ones. This step allows the user to select the main variables applying a theoretical system. 4) rating (multivariate risk analysis): After the selection of the main risk variables, the risk groups are defined and, consequently, it is possible to evaluate the tariff for each of them. This step allows the user to esimate the theoretical / commercial premium for each risk group and, if requested, the corresponding relativities. 5) comparison with the current tariff: The comparison between the premiums evaluated in step 4 and the current tariff can give useful information for underwriting risk selection. This step helps the user to perform this comparison in a simple way. In the following pages a more detailed description of the first version of the A.L. is reported, providing more information about each option and its output. VIDEO SCREEN EXPLANATION

3 SETS OF ANALYSES This screen represents the starting point of the A.L.: the user is asked to choose the guarantees and the type of vehicle to analyse from the relevant list box. The user must choose one of them (e.g. t.p.l., theft, fire, kasko for private cars) by simply clicking on the option preferred. ANALYSIS WINDOW This display screen represents the starting point of the risk analysis and its aim is to provide the user with a tool to get some general initial information about the risk. More precisely this display screen allows the user to analyse the risk by evaluating the

4 observed values of the most important risk indexes (claim frequency, average cost, pure premium, etc...) for each variable separately (univariate analysis) and for each couple of them (bivariate analysis).the results are presented both with numerical tables and with graphs (bars or rotating plots). The user is asked to choose the risk variables and the guarantees to make the chosen analysis, group the original categories into new classes for each variables, choose the type of analysis (univariate, bivariate, multivariate) and decide on the type of output. GROUPING This video screen allows the user to group the original categories into new classes for each variable. The grouping procedure can be manual or automatic. If the user wants to group the variables in his own way, he must choose the manual approach; if he wants to group the variables into homogeneous risk classes according to a statistical model, he must choose the theoretical approach. A mixed approach is also possible: the user can choose a theoretical approach and then modify the results manually. The automatic grouping creates homogeneous groups of classes for a certain variable using cluster analysis. The homogeneity within each group is referred to a chosen risk index and to a chosen guarantee, for example to the claim frequency for material damage.

5 UNIVARIATE ANALYSIS This screen shows the graphic and numerical representation of the univariate analysis. More precisely it allows the user to choose one risk variable (one at a time) and to analyse it calculating risk indexes (number of policies, claim frequency, average cost, pure premiums,...) and showing the relevant graphs (histogram). By simply double clicking on a bar of the histogram, it is possible to get information about the class (or group) to which the bar refers. BIVARIATE ANALYSIS

6 This screen shows the graphic representation of the bivariate analysis. The graph used is a 3D rotating plot and can give a visual idea of a possible correlation between two variables. It is even possible to see the numerical table concerning the usual risk indexes (claim frequency, average cost,...) regarding each possible combination of risk classes into two variables. MULTIVARIATE RISK ANALYSIS It s definitely the most important and sophisticated part of the Actuarial Laboratory because it performs the multivariate risk analysis, that is the evaluation of the risk taking into account all the correlations between variables. More precisely the multivariate analysis concerns both the selection of risk variables and the evaluation of the tariff for each class of risk. It is important to underline that even this step of the analysis allows the user to choose either a manual or a theoretical approach, following the philosophy of the software already mentioned above. In particular, the user can run the selection procedure in two different ways: - by asking the software to select the main risk variables and/or the main interactions according to a statistical model (the software starts the selection procedure by analysing them all together and cancelling the ones that are not considered important one by one according to the chosen significance level. At the end of the procedure only the significant variables remain in this list box). - by choosing manually his favourite variables and/or interactions. It is even possible to choose a mixed approach by modifying manually the result of the theoretical procedure. Rating is performed by estimating separately the claim frequency and the average claim cost and then multiplying them together. The reason for this is that their

7 probability distribution differs from one another completely and must be treated in two different ways. The critical success factor represents graphically the goodness of fit of the rating model. There are three areas: if the arrow is on the red area, the model does not fit the data well; if the arrow is on the yellow area, the model fits the data quite well; if the arrow is on the green area, the model fits the data well. PREMIUM ANALYSIS This screen allows the user to analyse the premium for each risk class one by one. More precisely, the table viewer contains the list of all the risk classes: each record corresponds to a different risk class according to the variables listed at the top of each column. The user, by simply moving the cursor, is able to view and compare the premiums (observed, estimated without relativities, estimated with relativities and commercial) related to each risk class. The four premiums are presented both numerically and graphically. The difference between the four types of premium is as follows: - the observed risk premium is calculated as a ratio between the observed total claim cost and the total number of vehicle year for each risk class. The observed risk premium is affected by the variability of the claim cost; consequently, in most of the cases it is very different from the other premiums; - the estimated risk premium without relativities is the risk premium estimated by applying the statistical model to the observed data and represents the unique and exact risk premium estimation; - the premium with relativities is the premium calculated by using the relativities that have been evaluated by applying the statistical model to the estimated risk premiums; - the commercial premium is the real premium applyed by the company to the relevant class of risk.