TITLE:
An Optimal Control Approach to Customer Lifetime Value
AUTHORS:
Darkhijav Bayanjargal, Batsukh Davaasuren
KEYWORDS:
Customer Lifetime Value, Acquisition Cost, Optimal Control
JOURNAL NAME:
iBusiness,
Vol.12 No.4,
December
23,
2020
ABSTRACT: It is very important for a company to determine
spending for acquisition and retention of customers which affect the Customer
lifetime value of the company. In this paper, we formulate the Customer
lifetime value model as an optimal control problem. The obtained problem is to
find an acquisition policy which maximizes the present value of all future
profits generated from a customer. Here the state variable is the average
margin for each customer about how much each customer contributes to the
company and the control variable is the cost of acquisition. We use the maximum
principle for optimality to solve the problem, estimate some parameters of the
problem using statistical data for Mobile service sector of Mongolia and
calculate the optimal Customer lifetime values of the sector for some values of
parameters.