Optimal capital and risk allocations for law- and cash-invariant convex functions

In this paper we provide a 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∈[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.

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