| 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. |