Determining Participatory and Exchange Contract's Optimal Share in the Interest- Free Banking

In the present article, besides examining the structure of interest-free banking and its methods of resource mobilization and allocation, we study and optimize the bank's behavior in the stochastic (indefinite) conditions. In other words, given the indefiniteness of account's profits and also of participatory contract's profits in the interest-free banking, the issue of stochastic calculus in mathematics is of a high usage in modeling these bank's behavior. In the present article, thus, using the stochastic optimal control technique, we examine the behavior of this kind of banks as an objective function, and identify, in the form of a theoretical model, that share of participatory and exchange contracts which maximizes the Islamic bank's share. Furthermore, we calculate the exchange rate elasticity and participation rate elasticity of contract's optimal share in the Iranian banking system.