On optimal intervention for customer lifetime value

The potential value of a customer to a commercial organisation can be a core ingredient in decision-making. There is a growing literature on the topic, much of it presented in rather general terms. In this paper, we examine a particular aspect, namely the expected income to the firm from a customer over his ‘lifetime’ (period of tenure with the firm). To derive quantitative results, we adopt a type of model in which there are underlying income and cost processes for a customer that evolve over time. In addition, we include a customer-specific effect that reflects the fact that some customers give rise to more income than others. These two stochastic elements are monitored by the firm for each new customer over an initial probationary period. Depending on the result of this assessment the firm might decide to offer a continuation of the account, perhaps on modified terms. The problem for the firm, which is the case addressed here, is to determine the length of the probationary period and the criterion for continuation. We set out a framework in which these two aspects may be optimised.