Стохастическая дискретная динамическая модель ликвидности банка

Abstract

Разработан алгоритм оценки программы привлечения депозитов для случайного гауссовского процесса. Получены уравнения для нестационарного коэффициента усиления фильтра Калмана. Приведены численные результаты, демонстрирующие устойчивую работу реализованного алгоритма фильтрации.

Розроблено алгоритм оцінки програми залучення депозитів для випадкового гауссівського процесу. Отримано рівняння для нестаціонарного коефіцієнта посилення фільтра Калмана. Подані чисельні результати демонструють стійку роботу реалізованого алгоритму фільтрації.

Introduction. For successful management of the banks’ deposit activity it is important to understand how to change the deposit attraction programme if the time structure of deposits has suddenly changed. The existing studies are mainly devoted to the analytical calculations of attracting programmes under conditions when the time structure of deposits is described by the continuous functions. There are scientific researches in which a methodology for calculating the deposit attraction programme are developed, provided that the time structure of deposits is discrete, which made it more similar to the problems that arise in each bank practice. However, in reality, the deposits attraction are outraged by random processes. Purpose. Therefore, the bank faces the task of assessing or forecasting a programme for attracting deposits under conditions of incomplete information (stochasticity). Methods. The task of evaluating the programme for attracting deposits under conditions of Gaussian noise is solved with the Kalman filtering procedure. Since the equation describing the discrete changes in the deposit attraction programme is a Voltaire difference equation of the convolution type, the Z-transformation is used to bring it to the standard representation in the state space. The scheme of the non-stationary Kalman filter is implemented in the form of a "predictor-corrector". Results. The algorithm for evaluating the programme for deposits attraction in the case of a random Gaussian process is developed. The equations for the non-steady-state Kalman filter are obtained. The numerical results clearly demonstrate the stable operation of the implemented filtering algorithm. Conclusion. The developed algorithm for estimating a discrete programme for attracting deposits in the presence of a random Gaussian process is useful for software developers at the banking institutions. Its usage helps to improve the decision-making system for banks’ deposit management. For future research, it is necessary to consider the random distortions described by Gaussian color or shot noise, when there are the rare but significant outliers of the balances on the bank’s correspondent account.