Deposit and Withdrawal Dynamics: A Data-Based Mutually-Exciting Stochastic Model

Abstract

This paper proposes a novel self- and mutual-exciting stochastic model to capture two essential features underlying a general type of discrete-time event data motivated by the practice: the dependence on the past event arrivals and associated sizes (i.e., self-exciting) and the behavioral interdependence between multiple activities (i.e., mutual-exciting). Despite the technical challenges in capturing these two features under a general discrete-time framework, we are able to fully characterize the probability distribution for the proposed model (i.e., the closed-form characteristic functions), theoretically quantify customer performance measures, and establish efficient maximum likelihood estimation. To illustrate the applicability of our model and validate its performance, we calibrate it with a customer deposit and withdrawal data set from one leading online money market fund. We analytically quantify the churn probability and expected activity level of customers as an illustration of performance measures and then compare our model with classic time-series and machine-learning models and show that our model can achieve high prediction accuracy. The theoretical tractability and predictive accuracy of the proposed framework enable us to build optimization models to improve firm performance, and we illustrate one application through a personalized interest-rate optimization problem. On a broader note, our model framework is generally applicable to characterize any discrete-time event data with self and mutual excitation in nature and to inform optimal policies for decision-makers.