Financial safety inequalities based on expected risks for credit institutions

Abstract

The stochastic mathematical model of the crediting process is examined. It is assumed that in unstable economical state the possible default of credit may be a reason of risk under the crediting. The fund value of the crediting is considered as some random variable that is changed step-wise at instants of the payments of a credits or at instants of their repayment. At the same time that process may be considered as a sum of the single impulse disturbances that appear at the random instants and are characterized by a set of parameters that may be random too. These parameters are determined by the conditions of crediting. Among them a value of loan, a term of loan, the interest rate of crediting, a payment tariff of overdue repayment, a time of repayment delay, the probability of loan repayment by borrower. It is considered that credit institution sets a boundary admissible level of the loss for security of expenses discharge and receipt of guaranteed gain. By assumption that different random variables are independent the expected risk of crediting for a single loan is found. On base of the expected risk formula the inequalities are derived to determine the values of above parameters that guarantee the increase of the expected value of crediting fund. Numerical results are brought.