A decision theoretic framework for profit maximization in direct marketing

One of the most important issues facing a firm involved in direct marketing is the selection of addresses from a mailing list. When the parameters of the model describing consumers' reaction to a mailing are known, addresses for a future mailing can be selected in a profit-maximizing way. Usually, these parameters are unknown and have to be estimated. These estimates are used to rank the potential addressees and to select the best targets.

Several methods for this selection process have been proposed in the recent literature. All of these methods consider the estimation and selection step separately. Since estimation uncertainty is neglected, these methods lead to a suboptimal decision rule and hence not to optimal profits. We derive an optimal Bayes decision rule that follows from the firm's profit function and which explicitly takes estimation uncertainly into account. We show that the integral resulting from the Bayes decision rule can be either approximated through a normal posterior, or numerically evaluated by a Laplace approximation or by Markov chain Monte Carlo integration. An empirical example shows that indeed higher profits result.