Review of Quantitative Finance and Accounting

, Volume 52, Issue 4, pp 1043–1064 | Cite as

A Markov decision model for consumer term-loan collections

  • Zhixin Liu
  • Ping HeEmail author
  • Bo Chen
Original Research


We examine how to efficiently schedule collection actions for consumer term-loan accounts over time using a Markov decision model. A consumer loan account at each age can be classified into different account states, including current, delinquent, early payoff, default, and bankrupt. We model state transitions of loan accounts using a Markov transition matrix, and develop an optimization method to determine the collection action at each state and age for each consumer type to maximize the lender’s expected value. The optimization approach incorporates default risk and operational cost, and also addresses the time value of money, the tradeoff between interest revenue and borrowing cost, time consistency in optimization, competing risks between different account states, and penalty for late payment. Compared with a static collection policy, our method is demonstrably more valuable for accounts with high interest rates and medium to high loan amount, especially with stronger collection effects. We also demonstrate how the collection actions implemented under an optimal collection policy are affected by interest rate, loan amount, and collection effects.


Dynamic programming Collection Markov process Optimization 

JEL Classification

G21 G23 



We sincerely thank the two anonymous reviewers for their valuable comments, which have significantly improved the quality of this work. The work of the second author is partly supported by the National Natural Science Foundation of China (No. 71571159).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Management Studies, College of BusinessUniversity of Michigan–DearbornDearbornUSA
  2. 2.School of Business AdministrationSouth China University of TechnologyGuangzhouPeople’s Republic of China
  3. 3.School of ManagementHefei University of TechnologyHefeiPeople’s Republic of China

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