Optimal customer selection for cross-selling of financial services products

A new methodology, for optimal customer selection in cross-selling of financial services products, such as mortgage loans and non life insurance contracts, is presented. The optimal cross-sales selection of prospects is such that the expected profit is maximized, while at the same time the risk of suffering future losses is minimized. Expected profit maximization and mean–variance optimization are considered as alternative optimality criteria. In order to solve these optimality problems a stochastic model of the profit, expected to emerge from a single cross-sales prospect and from a selection of prospects, is developed. The related probability distributions of the profit are derived, both for small and large portfolio sizes and in the latter case, asymptotic normality is established. The proposed, profit optimization methodology is thoroughly tested, based on a real data set from a large Swedish insurance company and is shown to achieve considerable profit gains, compared to traditional cross-selling methods, which use only the estimated sales probabilities.