A mathematical programming approach to optimise insurance premium pricing within a data mining framework
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#2002 Operational Research Society Ltd. All rights reserved. 0160-5682/02 $15.00 www.palgrave-journals.com/jors
A mathematical programming approach to optimise insurance premium pricing within a data mining framework AC Yeo1, KA Smith1*, RJ Willis1 and M Brooks2 1
Monash University, Australia; and 2Australian Associated Motor Insurers Limited, Australia
In this paper we provide evidence of the benefits of an approach which combines data mining and mathematical programming to determining the premium to charge automobile insurance policy holders in order to arrive at an optimal portfolio. An non-linear integer programming formulation is proposed to determine optimal premiums based on the insurer’s need to find a balance between profitability and market share. The non-linear integer programming approach to solving this problem is used within a data mining framework which consists of three components: classifying policy holders into homogenous risk groups and predicting the claim cost of each group using k-means clustering; determining the price sensitivity (propensity to pay) of each group using neural networks; and combining the results of the first two components to determine the optimal premium to charge. We have earlier presented the results of the first two components. In this paper we present the results of the third component. Using our approach, we have been able to increase revenue without affecting termination rates and market share. Journal of the Operational Research Society (2002) 53, 1197–1203. doi:10.1057/palgrave.jors.2601413 Keywords: data mining; insurance; clustering; neural networks; integer programming; optimisation
Introduction To succeed in a highly competitive environment, insurance companies strive for a combination of market growth and profitability, and these two goals are at times conflicting. Premiums play a critical role in enabling insurance companies to find a balance between these two goals. The challenge is to set the premium so that expected claim costs are covered and a certain level of profitability is achieved, yet not to set premiums so high that market share is jeopardized as consumers exercise their rights to choose their insurers. This problem is akin to portfolio optimisation where an investor strives to find a balance between risk and return across their portfolio of investments.1 In the insurance optimisation problem, as premiums increase, termination rates also increase, resulting in loss of market share. The insurer strives to strike a balance between market share and revenue across the portfolio of policy holders. Insurance companies have traditionally determined premiums by assigning policy holders to pre-defined groups and observing the average claim behaviour of each group. The groups are formed based on industry experience about the perceived risk of different groups of policy holders. With the advent of data warehouses and data mining however *Correspondence: KA Smith, School of Business Systems, Faculty of Information Technology, PO Box 63B, Monash University, Vi
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