Short note on inf-convolution preserving the Fatou property

Abstract

We model agents’ preferences by cash-invariant concave functionals defined on L∞, and formulate the optimal risk allocation problem as their infimal-convolution. We study the case of agents whose choice functionals are law-invariant with respect to different probability measures and show how, in this case, the value function preserves a desirable dual representation (equivalent to the Fatou property).