Markov Chain Model

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MODELING CUSTOMER RELATIONSHIPS
AS MARKOV CHAINS
Phillip E. Pfeifer
Robert L. Carraway f INTRODUCTION
The lifetime value of a customer is an important and useful concept in interactive marketing. Courtheaux (1986) illustrates its usefulness for a number of managerial problems—the most obvious if not the most important being the budgeting of marketing expenditures for customer acquisition. It can also be used to help allocate spending across media (mail vs. telephone vs. television), vehicles (list A vs. list B), and programs (free gift vs. special price), as well as to inform decisions with respect to retaining existing customers (see, e.g., Hughes, 1997). Jackson
(1996) even argues that its use helps firms to achieve a
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They offer five such mathematical models, couched in the Dwyer customer retention/migration classification scheme. While
Dwyer illustrates the calculation of LTV using two extensive numerical examples, Berger and Nasr provide mathematical equations for LTV for five situations—four involving customer retention and one involving customer migration.
Blattberg and Deighton (1996) also formulate a mathematical model for LTV, for the purpose of helping managers decide the optimal balance between customer acquisition spending (investments to convince prospects to become customers) and customer retention spending (investments to convince current customers to continue purchasing from the firm).
Whereas the Berger and Nasr models apply only to customers (people or organizations who have already purchased from the firm), the Blattberg and Deighton model applies specifically to prospects (people or organizations who have yet to purchase from the firm). Because the Blattberg and Deighton model uses an infinite horizon, their resulting equation for LTV is quite simple and easy to evaluate, and involves none of the summation operators on which the Berger and
Nasr finite-horizon models rely.
This paper builds directly on the work of
Berger and Nasr (1998) and Blattberg and
Deighton (1996) in that it introduces a general class of mathematical models, Markov Chain
Models, which are appropriate for modeling customer relationships
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