Lorenz Curve for Profitable Insurance Portfolio Management

University essay from KTH/Matematik (Avd.)

Abstract: Since its introduction by Max Otto Lorenz, the Lorenz curve has been utilizedin several financial contexts. By using regression analysis to approximate theclaim cost of policyholders, a vector consisting of policyholder characteristics canbe obtained. The ordered Lorenz curve can subsequently be used to understandwhat commonalities are shared between profitable policyholders. This allows forbetter management of the insurance portfolio and thus better customer relationstowards both the policyholders and the insurer, which is important for an insuranceconsultancy agency. The aim of this thesis was to investigate which attributesapproximate the policyholder claim costs and consequently obtain insight into whatattributes are shared among profitable portfolio clients. The results presented inthis thesis show that a multi-linear regression model, transformed using the Box-Cox method is insufficient to approximate the claim costs in a convincing manner.The model obtained in the thesis was capable of identifying significant regressorsbut the overall result displayed uncertainties in regards to overall goodness of fit.This means that the variability explained by the regression model only represents4.95% of the variability in the claim cost data. Thus, the relativity measureintroduced in section 2.1.1 was deemed uninterruptible in a meaningful way.Consequently, the empirical distribution functions presented in section 1.1 wouldbe based on a faulty order statistic, and in turn the visualization of an orderedLorenz curve with such a relativity measure is unnecessary.

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