A Cooperative Value in a Multiplicative Model

In this study, we consider positive cooperative TU games with finitely many players. We assume that all agents use the same scale. Furthermore, the worth that a coalition of players can achieve by cooperation is measured as a multiple of a defined standard base. In this multiplicative setting we characterize and analyze a solution concept which is related to the well known Shapley value. From a statistical point of view, the methodology allows computing relative importance of individual factors on the expected value. In particular, we present a specific application to general insurance pricing. As a result, the value may be used to analyze the business mix of an insurance portfolio by measuring exposure to risk factors. Similar applications refer to credit scoring and customer relationship management. In this sense, the modelling approach may be embedded as a risk analysis technique within a risk management framework