Abstract: Recently, the customer relationship management has become the main strategy of marketing, and customer lifetime value plays a key role in customer relationship management. Based on the censored  δ  shock model and its marked process, the probability distribution of customer lifetime of homogeneous Poisson marketing system was discussed, and the expectation, second moment and variance of the instantaneous customer lifetime value and the total customer lifetime value were obtained.

Key words: Poisson marketing system, customer lifetime, customer lifetime value, customer lifetime value, mathematical relationship marketing