The Effects of Fixed Return Instruments on Investment Decisions in Islamic Economics: Using Stochastic Mathematical Model

In the Islamic economics, when we want to deal with investment decisions, we should determine that what proportion of wealth should allocate to risky asset and what proportion to fixed income instruments like Murabahah and Ijarah Sukuk. Theoretically, Islamic fixed return instruments and conventional risk free bonds are completely different from each other, since the investor of Sukuk actually buys the underlying asset and has some ownership risks. But in practice, it is usually believed that these risks would decline the satisfaction level of investors, and so, financial institutions provide Sukuk in such a way that they are very similar to conventional bonds. In this paper, we want to analyze the effect of Islamic fixed return instruments on the investment decisions when they have no risk in one case, and when the investor face the risks in these instruments in the other case. For this purpose, we construct a stochastic investment-consumption optimization model for each case and solve it to find the optimal path of variables overtime. To compare the results of different cases, we assumed some hypothetical values for the parameters and calculated the numerical path of variables over time. The results show that, the model which considers the risky characteristics of Sukuk brings more utility and welfare to the investor comparing to the model that considers Sukuk as risk free instrument.