Fair sharing ratios of Profit and Loss sharing contracts

TL;DR

This paper introduces a new concept of c-fair profit sharing ratios in Islamic Profit and Loss sharing contracts, linking them to economic factors and project success, with adaptable modeling approaches.

Contribution

It proposes the notion of c-fair profit sharing ratios and explores their relation to economic factors, providing a flexible framework for computation using econometric or stochastic models.

Findings

New c-fair profit sharing ratios concept

Relation between ratios and economic factors elucidated

Framework adaptable to various econometric models

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.