Optimal scoring cutoff policies and efficient frontiers

Multiple business objectives are increasingly important in determining account acquisition and management policies in scored retail credit and loan portfolios. These business objectives include profit and market share, as well as the more traditional management of risk. We formulate a mathematical model that addresses the problem of how acquisition decisions should be made with multiple, conflicting objectives when one, or more than one, scorecard is available to the portfolio manager. We show that iso-contours for expected profit, volume and loss are straight lines in the receiver operating characteristic (ROC) space and develop results that establish equivalence between ROC dominance, maximum expected profit, and efficient-frontier dominance in the space of multiple business measures. For two non-dominating scorecards, we derive the efficient frontiers in the profit-volume space and provide guidelines for choosing optimal policies based on the decision maker's trade-offs between objectives.