Simple computing of the customer lifetime value: A fixed local-optimal policy approach

In this paper, we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value. The method is developed for a class of ergodic controllable finite Markov chains. We propose an approach based on a non-converging state-value function that fluctuates (increases and decreases) between states of the dynamic process. We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy. Then, we provide an analytical formula for the numerical realization of the fixed local-optimal strategy. We also present a second approach based on linear programming, to solve the same problem, that implement the c-variable method for making the problem computationally tractable. At the end, we show that these two approaches are related: after a finite number of iterations our proposed approach converges to same result as the linear programming method. We also present a non-traditional approach for ergodicity verification. The validity of the proposed methods is successfully demonstrated theoretically and, by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.