Abstract:The main aim of the presentation is to discuss methods which can

Modelling the number of daily road accidents can be beneficial not only for insurance companies but also for other institutions such as the national road administration, national insurers' bureau etc. Accurate predictions of the number of road accidents could be beneficial in terms of efficient liquidation planning, improving the reserving processes, streamlining the capital allocation and road maintaining. Consequently, it is relevant to build a viable model for predicting the number of daily road accidents. One of the most important parts of the model is the model of daily seasonality. Since this seasonality exhibits a long seasonal period, approaches based on basis expansion can be used for its modelling. We also investigate the multiple seasonality pattern and specific time events which could potentially affect the number of accidents. Furthermore, the impact of different external variables, such as the average daily temperature, rainfall and other factors influencing human driving skills, will also be investigated.

The economic datasets have their specifics; they usually describe human behavior or activity, which are difficult to measure. Thus, in comparison to non-economic datasets, they are less consistent. The paper analyzes differences between categorical economic and non-economic datasets in hierarchical clustering (HCA). To achieve this goal, two analyses based on 25 realworld datasets are carried out. In the first one, groups of economic and non-economic datasets are compared from the point of view of their internal characteristics based on HCA results; in the second one, homogenous groups of datasets are recognized and they are further examined by internal characteristics and graphical outputs. For each group of datasets, the most appropriate similarity measures are identified. The results show substantial differences between economic and non-economic datasets, primarily in terms of the within-cluster variability decrease. We were also successful in classification of the examined datasets into easily interpretable groups, for which suitable similarity measures were identified.

Valuation of the insurance portfolio is one of the essential actuarial tasks. Life insurance valuation is usually based on a projection of cash flows for each policy which is demanding computation time. Furthermore, modern financial management requires multiple valuations under different scenarios or input parameters. A method to reduce computation time while preserving as much accuracy as possible based on cluster analysis is presented. The basic idea of the method is to replace the original portfolio by a smaller representative portfolio based on clusters with some weights that would ensure the similarity of the valuation results to the original portfolio. Valuation is then significantly faster but requires initial time for clustering and the results are only approximate – different from the original results. The difference is studied for a different number of clusters and the trade-off between the approximation error and calculation time is evaluated.

This paper thoroughly examines three recently introduced modifications of the Gower coefficient, which were determined for data with mixed-type variables in hierarchical clustering. On the contrary to the original Gower coefficient, which only recognizes if two categories match or not in the case of nominal variables, the examined modifications offer three different approaches to measuring the similarity between categories. The examined dissimilarity measures are compared and evaluated regarding the quality of their clusters measured by three internal indices (Dunn, silhouette, McClain) and regarding their classification abilities measured by the Rand index. The comparison is performed on 810 generated datasets. In the analysis, the performance of the similarity measures is evaluated by different data characteristics (the number of variables, the number of categories, the distance of clusters, etc.) and by different hierarchical clustering methods (average, complete, McQuitty and single linkage methods). As a result, two modifications are recommended for the use in practice.