  We consider a financial model where the prices of risky assets are quoted by
a representative market maker who takes into account an exogenous demand. We
characterize these prices in terms of a system of BSDEs with quadratic growth.
We show that this system admits a unique solution for every bounded demand if
and only if the market maker's risk-aversion is sufficiently small. The
uniqueness is established in the natural class of solutions, without any
additional norm restrictions. To the best of our knowledge, this is the first
study that proves such (global) uniqueness result for a system of fully coupled
quadratic BSDEs.
