Axiomatic risk sharing and capital allocation

We aim to share risky endowments among finitely many agents, subject to liquidity constraints. We axiomatically characterize baseline solutions, which use a baseline vector of fixed contributions and a rationing method. We propose a general fairness condition, that uniquely determines these fixed contributions. The fairness condition is flexible enough to allow for the use of any capital allocation rule. One rule stands out as a K-fair solution: the one implied by the constrained egalitarian rationing rule. It is the unique rule satisfying a lower bound on taking part of the risk, a composition property, and null consistency. Furthermore, we provide two more characterizations of this rule; one based on local symmetry and one based on minimax expected contributions under truncation.