Abstarct: In recent years, corporations realized that customers are not profitable for them alone. The development of relationships with the profitable customers in a crucial factor in staying in the market. Marketing is the art of attracting and keeping profitable customers. The customer lifetime value (CLV) is a prediction of the net profit attributed to the entire future relationship white a customer. In the thesis we consider the discrete and continuous CLV. First we introduce some models of CLV and its applications, then markov decision process is used to optimization CLV. Finally, in the case that the relationship of company and customer is in a continuous time the optimal time to reviewed account is discussed.