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Analytic Solutions of a Stochastic Banking Model with Left Truncated Inter Withdrawal Times and Upper Truncated Amount of Withdrawals

Author : G.S.Devasena

Pages : 2519-2522
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Stochastic Banking models (S.B.Ms) occupy an important place in modern research, dealing with cash flow analysis of a Banking System. Knowledge about the reserve level of a Banking system, play a vital role in many Fiscal policies of any economy. To have prospective and fruitful economic plans, one must have a prior knowledge about the cash reserve level available with the nation, without which the plans will be vague and ineffective. Hence in 1983 (Sarma, 1983) proposed a stochastic banking model (S.B.M) with a critical reserve level (C ≥ 0) and obtain many results relating to the reserve level X(t) available with the system at any given time t ≥ 0, (vide Ref .2). Later in 1991, (Sarma and Pushpangali ,1991) Proposed a S.B.M.with general linear rate of inputs and obtained explicit expressions of M/G/1/FIFO/K and G/M/1/FIFO/K S.B.Ms. Further in 1995,(Sarma and Sarma, 1995) obtained results of S.B.Ms where withdrawals or inter – withdrawals are assume to follow an Erlangian distribution. The application of this distribution to S.B.M.has more practical relevance because the service of a customer in a Bank consists of different phases like issuing of tokens, passing of the amount, making suitable entries and so on. Thus more and more practically relevant assumptions were brought in to the model, so that the S.B.M. suggested in 1983 is more and more closer to the reality.
In this paper a practically valid and more essential assumption namely (1) Lower Truncation Of Inter – Withdrawal Times And (2) Upper Truncation Of Amounts Of Withdrawals, is incorporated into the Stochastic Banking Model in order to make the model more closer to reality and to increase the application potentiality of the model. In General a customer is not allowed to withdraw or take loan against the amount deposited by him in the form of fixed deposits, until a minimum pre – stipulated time is over. Further, he cannot withdraw the entire amount deposited by him as Loan. Only a certain percentage of amounts are sanctioned to the customer which is generally known as eligible amount for the loan and he is eligible to withdraw the amount as loan up to an maximum of that eligible amount An analytic solution of a MT/Ma/1/FIFO/∞ Stochastic Banking Model (S.B.M) is obtained, Where MT represents a lower truncated Law governing the random variable of inter – withdrawal times and Ma represents a upper truncated Law governing the random variable of amount of withdrawals.

Keywords: Lower Truncated Variable, Upper Truncated Variable, Reserve level of a Bank, Stochastic Banking Models, Critical reserve level.

Article published in International Journal of Current  Engineering  and Technology, Vol.4,No.4 (Aug- 2014)



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