Numerical simulation of stochastic model for deposit and loan volume based on the Lotka - Volterra model

Abstract

Lotka - Volterra model is often used to model the interaction between prey and predator, where the existence of predators depends on the presence of prey. In this paper, Lotka - Volterra model is used to describe the interaction between the volume of deposits and loan. It can be interpreted as the interaction between prey and predators in which deposit as prey and loan as predator. Interaction between Deposit and Loan volume model is expressed in a system of stochastic differential equations, which is derived from the Deterministic Lotka-Volterra model. Unlike in deterministic model, in this stochastic model, the volume of deposit and loan are stochastic variables and a random noise may occur in their interactions. The parameters in the model will be approximated using the Least Squares method for some financial data. The solution of the stochastic model is approximated using Euler-Maruyama method. The simulation of the stochastic models of the deposit and loan volume can represent the perturbation between the deposit and loan volume, and the results will be compared with the financial statement data per month from a commercial bank in Indonesia from 2003 until 2013.