Ranking functions, perceptrons, and associated probabilities
KES'05 Proceedings of the 9th international conference on Knowledge-Based Intelligent Information and Engineering Systems - Volume Part III
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The paper is motivated by a ranking problem arising in financial institutions (classifying customers according to increasing creditworthiness using a generalized perceptron) and the particular form of the associated probabilities resulting from its solution. Similar forms of the probabilities have been obtained using rather different approaches. It is shown that if the relevant parameters are determined experimentally they can be exploited to compute optimal (in the sense of expected maximal profit) interest rates. Somewhat surprisingly it turns out that under weak additional assumptions in all cases there is a unique finite optimum if a simple linear model is used ("Greed doesn't pay"?). For a special case that frequently arises in practice an explicit upper bound is obtained. In addition it is shown that knowledge of a single parameter suffices to compute the corresponding interest rate.