Abstract: The resolve solution to the expected net present value equation of a kind of Markov model（Pfeifer model），in infinite horizon purchasing cases，is given，in order to make easer to the study and analysis of such problem.Such model is always used in the study on Customer Relationship Management（CRM） problem.Based on the matrix inverse formula，the inverse matrix is decomposed and simplified，its resolve solution is computed，and the resolve solution for the expected net present value vector for such kind of Markov model V=（I-P）^-1R is found，then the solution suited for the n order case is expended.Based on the computed result，a short further analysis and discussion to its CLV（the total expected net present value in customer life cycle） is made.The resolve solution to the expected net present value will supply an easy study base to such kind of problem analysis.

摘要： 给出了用于研究客户关系管理（Customer Relationship Management，CRM）模型中的一类马氏链数学模型（Pfeifer模型）的收益期望值的解析解（无限次交易条件下），以方便该类模型的研究和分析。借助于求逆公式，将V=（I-P）^-1R方程中矩阵求逆部分进行分解和简化，解出矩阵逆的解析解，从而求解出该类模型收益期望值向量的解析解，并推广到n阶。基于该解析解，对该类模型收益总期望值的特性进行了简单分析和讨论，该收益期望值的解析解将给该类方程的解析分析提供帮助。