Module 11:Application of stochastic processes in areas marketing
  Lecture 37:Application of renewal theorey in Marketing with examples
 

Thus matrix  is a simple yet effective way of summarizing the customer's recency for  time periods. Furthermore depending on the concept of next present value of contribution and spending we may depict the reward matrix of company with respect to this customer as shown below:

Table 11.3: Reward matrix for the company depending on one customer

 

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1

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In case the company is interested to find the expected profit for this scenario, then we need to calculate the following which is given by  and that is shown below:

Table 11.4: Matrix for expected value earned by the company depending on one customer

 

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2

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Thus for an infinite time zone consideration we need to find , which will give a lot of information to the company about customer retention and his/her life value.