# Short Note on Inf-Convolution Preserving the Fatou Property

## Abstract

We model agents’ preferences by cash-invariant concave functionals defined on L^{\infty}, 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).

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