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Activity Number:
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364
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Type:
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Contributed
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Date/Time:
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Tuesday, August 4, 2009 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Statistics and Marketing
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| Abstract - #304844 |
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Title:
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A Geometric Brownian Motion Model of Purchase History Dynamics
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Author(s):
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Kalyan Raman and Edward C. Malthouse*+
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Companies:
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Northwestern University and Northwestern University
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Address:
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1870 Campus Drive, Evanston, IL, 60208,
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Keywords:
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Markov Process ; Lifetime Value ; Customer Equity ; Ito's Lemma ; Database marketing ; CRM
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Abstract:
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We propose a Markov process to model customer lifetime value. We assume that the growth rate of the odds ratio of future purchases fluctuates randomly around a deterministic mean that is a function of marketing activities and other predictive variables such as RFM, derive a stochastic differential equation for the odds ratio, solve it through an application of Ito's lemma, and show that the odds ratio evolves as a log-normal process. Empirical analyses validate our model. Unlike earlier work that exogeneously fits log-normal distributions, log-normality is a consequence of our fundamental assumption about the growth of the odds ratio. We derive the transition probability distributions of the stochastic odds ratio process and show how to derive the steady-state probability distribution for the odds ratio process. Marketing applications are discussed.
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