A Mathematical Profit-Sharing Model for Mudaraba Sukuk Financing

Abstract

Sukuk is one of the popular financial instruments today. However, existing return distribution mechanisms do not explicitly reflect the dynamics of investment profitability. This study develops a mathematical profit-sharing model for a mudaraba sukuk financing scheme that implements periodic return distributions linked to the profitability of the underlying investment. Geometric Brownian Motion is employed to generate investment income and represent its dynamics, while investment returns are determined using a time value of money approach adapted to the sukuk financing structure, and sensitivity analysis is conducted under varying profitability conditions. The simulation results demonstrate that the proposed model can implement periodic profit-sharing distributions while ensuring principal repayment at maturity. This model offers a mathematical perspective on sukuk research and contributes to the existing literature on mathematical finance.