A Mathematical Model of the Profit-Loss Sharing (PLS) Scheme

In financial world, lending money is a part of investment where the borrower get an opportunity to start up or enlarge their business, and as in the fair world, the lender should also take profits on the borrower's investment. In Islamic finance, the profit (and later also the loss) of an investment is coming from the profit-loss sharing concept. We proposed a mathematical model of micro-credit scheme based on this concept. The model is implemented onto real data taken from some low income Indonesian traders and the simulated one. We deliberately choose these respondents due to they are traditionally targeted by usurers (or rentenir in Indonesian) who lend money with high interest rate and penalties so, in many cases, it will makes them broke instead of having their business improve. The important issues in the model are how to generate the simulated data representing the real data, determination of required parameters and to find an optimal portion of profit share which is quite fair for the lender and the borrower. The model shows that the borrower will benefit from the scheme even though sometimes she has losses in particular days, and the lender will get good return as an investment return.