  We consider the risk sharing problem for capital requirements induced by
capital adequacy tests and security markets. The agents involved in the sharing
procedure may be heterogeneous in that they apply varying capital adequacy
tests and have access to different security markets. We discuss conditions
under which there exists a representative agent. Thereafter, we study two
frameworks of capital adequacy more closely, polyhedral constraints and
distribution based constraints. We prove existence of optimal risk allocations
and equilibria within these frameworks and elaborate on their robustness.
