We consider a one period (two time points-) model of efficient risk sharing, when the risk of possible sharing rules are constrained to be linear. This can be interpreted as a model of a market for common stocks. Here we study the properties of a competitive equilibrium in an incomplete market. The lack of Pareto optimality is then the typical case. We do characterize, however, the situations where the competitive financial equilibrium is also Pareto optimal, and illustrate by examples. Since the marketed subspace M is a closed, linear subspace of L2, we employ Hilbert space techniques in finding the first order conditions. We conclude with a discussion of the different features of idiosyncratic risks in insurance, and risks in financial markets, where a common ground is suggested.