Paper: arXiv 2507.01995

Authors: Abass Sagna

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.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical generalization of fair profit-sharing ratios in Islamic finance (Mudharabah, Musharakah, and Wakalah contracts) using payoff expectations and stochastic formulations. However, it is primarily analytical and conceptual, lacking empirical backtesting or real-world data validation.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Determine 'c-fair' Profit & Loss (PL) sharing ratios based on partner contributions"] --> B["Inputs:<br>Investment risk, labor, capital, & contribution rates c = (c1, ..., cd)"]
    B --> C["Methodology:<br>Model PL sharing & agency contracts via stochastic diffusion models"]
    C --> D["Computation:<br>Calculate/approximate expected maturity payoffs for each partner"]
    D --> E["Outcomes:<br>Connect sharing ratios directly to real economy factors & quantify partner payoffs"]