Dynamic cash management models

Zhang, Zimian and Kirkbride, Christopher (2022) Dynamic cash management models. PhD thesis, Lancaster University.

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Abstract

Classical cash management models concern how an organisation should maintain their (liquid) cash balances in order to meet cash demands over time. In these models the balance can be increased or decreased to offset penalties for not being able to meet a cash demand or the opportunity cost of holding too much cash, respectively. The external source from which this money comes from or is sent to is not explicitly modelled but is assumed to be available at all times. In this thesis we contribute to the cash management problem by discussing three novel cash management models. To begin with, we include a second asset to the cash management model and assume the cash inflows are generated from this asset. We formulate this problem as a discrete Markov decision process (MDP) and solve it by the classic backward iteration method. We show that the optimal cash policy for this model possesses the two-threshold two-target form. Moreover we observe that the agent should take a ‘safer’ cash policy when the company has a balanced cash inflows and outflows. Then we introduce loan opportunities to the model. In this problem, we allow the agent taking loans from financial intermediates. We assume there is one type of unsecured loan with fixed interest rate and the manager can take this loan repeatedly once his previous debt is paid off. We also solve this model via the discrete MDP approach. Moreover we propose a heuristic for this problem based on the policy improvement which is shown to perform strongly in our experiments. At last, we consider an agent managing a cash account and a number of as- sets accounts. Hence both cash policies and asset allocation policies are studied simultaneously. Moreover we assume the agent wishes to pursuit the net profits while controlling the risk associated with his management strategies. We solve this model using a separable Piecewise linear approximate dynamic programming approach. We also provide a heuristic based on the myopic greedy algorithm and the discrete MDP approach as benchmarks. The numerical experiments show that the PWL ADP outperforms the heuristic in terms of objective values and takes significantly less solution time comparing with the discrete MDP.