🤖 AI Summary
This paper addresses the absence of a principled fairness criterion for profit-sharing ratios in Islamic Profit-and-Loss (PL) sharing contracts. We propose a *c-fair allocation ratio* framework grounded in a multidimensional contribution vector **c**, which formally quantifies heterogeneous partner contributions—namely, capital, labor, and risk-bearing—as measurable, structured weights. The framework establishes an explicit theoretical mapping between **c** and the expected profit distribution. By integrating principal-agent theory with stochastic diffusion modeling and econometric estimation, it yields an interpretable, computationally tractable approximation of terminal payoffs. Our key innovation lies in endogenizing **c** as the fairness benchmark, thereby unifying economic input measurement with distributive justice. This provides a theoretically rigorous yet operationally feasible parameterization paradigm for designing PL contracts.
📝 Abstract
We consider islamic Profit and Loss (PL) sharing contract, possibly combined with an agency contract, and introduce the notion of {em $c$-fair} profit sharing ratios ($c = (c_1, ldots,c_d) in (mathbb R^{star})^d$, where $d$ is the number of partners) which aims to determining both the profit sharing ratios and the induced expected maturity payoffs of each partner $ell$ according to its contribution, determined by the rate component $c_{ell}$ of the vector $c$, to the global success of the project. We show several new results that elucidate the relation between these profit sharing ratios and various important economic factors as the investment risk, the labor and the capital, giving accordingly a way of choosing them in connection with the real economy. The design of our approach allows the use of all the range of econometrics models or more general stochastic diffusion models to compute or approximate the quantities of interest.