Optimal Capital and Risk allocation for law and cash invariant functions, Finance and Stochastics

In this paper we provide the complete solution to the existence and characterisation problem of optimal capital and risk allocations for not necessarily monotone, law-invariant convex risk measures on the model space Lp, for any p ∈ [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. Key words: exact convolutions, law-invariant risk measures, optimal capital and risk allocations.