Markov chain model has been recently used for the collection management of accounts receivable.
Cyert, Davidson and Thompson (C-D-T) model is one of the representative stationary models, which includes transition matrix with (n+1) transient states and two absorbing states of payment and bad debt and estimates the collection ratio from the limiting behavior of the stationary Markov chain.
In this thesis, using alpha potential matrix and the expected absorbing time to payment state, the present value of the collected amount, instead of the simple collection ratio, is calculated. This Markov chain model with present value vector can be used to decide the optimal discount rate which is one of the most important variables of collection policy.
For nonstationary model, each element in transition matrix changes every moment. It is needed to predict the value of the element in next period, which is estimated from the regression equation between the collection ratio of the aging balance in prior period and in current one.
The numerical results show that the nonstationary Markov chain model with regression improves the accuracy of the prediction, which make it easy to manage the liquidity of a firm. Simulation of the liquidity management policy with the regression method result in the 14% reduction in interest expense.