In this paper, the model
formulated incorporated stochastic variables such as bank loans and deposits as
well as some deterministic variables: cash available, depreciation, capital
expenditure, tax and costs, comprising variable costs and fixed costs. This
paper assumes that the dynamics of bank loans and deposits at time t follow a geometric Brownian motion,
therefore, it satisfies certain stochastic differential equations (SDEs)
formulated on some probability space. On the other hand, the growth rate μL(t) in loan at time t, growth rate μD(t) in deposit at time t, and the variable cost η(t) at
time t are assumed to be driven by
mean-reverting Ornstein-Uhlenbeck processes. The SDEs of the dynamics of bank
loans, growth rate in loans, bank deposits, growth rate in deposits and
variable cost arising from the model were solved by means of the ItÔ Lemma. Discrete
time approximations of the exact solutions of the SDEs were derived and used in
a Monte Carlos simulation software.
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