Analysis
and Planning

The analysis of groups of savers that form a saving collective and forecasts based on the results have formed an important issue in the mathematics of public loan banking and the special issues of liquidity planning, product care and development. We try to build models that simulate the behavior of owners of saving contracts and predict their future behavior. As a further development of these models we currently apply cluster analysis methods to our data. New methods of combinatorical optimization are used to improve the socio-economic analysis of the stock of contracts and savers.

Since we have to deal with large amounts of data innovative methods of  Data analysis had to be applied. Further insight can be gained by our articles in the  Annual Report 95/96  and  Annual Report 97/98  (both in German only).

In our projects we often encounter problems that can only be solved by a thorough mathematical analysis. People who are interested in topics for diploma theses or dissertations may visit our  Themenbörse (still German)   and/or contact us.

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The idea of public loan banking and our investigation methods

In order to finance a building and loan association it is an important issue to know the structure of the whole group of savers, called a collective. Detailed analysis of the large amounts of data has become manageable in recent time only by the development of faster computers with larger memory. With new hardware methods and new mathematical methods we try to analyze the saving behavior of typical savers. At the same time we apply methods of cluster analysis to determine groups of savers with similar saving behavior. Most of the known cluster algorithms that we found are constrained to pools of 50 to 100 items and only a few features, whereas in our problem we have to deal with up to 2.5 million items and about 50 features. The goal of our cooperation with the building and loan association is the development of tools to analyze and predict the amount of savings over time based on the saving behavior of the past and current savers in the collective. Our knowledge is built into simulation models that predict the behavior of the collective. At the same time we gain insight into real saving behavior. To predict short-term and medium-term developments the principal influence is given by the current collective. Long-term predictions require an extrapolation of the current development of the collective together with external influences. The following simulation models have been developed in our group in three phases:

• The slice model (Clustering by contracts)
• The micro simulation model (Extrapolation of single bank accounts)
• The mesoscopic model (Groups of contracts based on single accounts)