Optimal Capital and Risk Allocations for Law-and Cash-Invariant Convex Functions

In this paper we provide the complete solution to the existence and characterization problem of optimal capital and risk allocations for not necessarily monotone, law-invariant convex risk measures on the model space Lp, for any p ε [1;∞]. Our main result says that the capital and risk allocation problem always admits a solution via contracts whose payoffs are defined as increasing Lipschitz continuous functions of the aggregate risk.