  We consider the problem of optimally sharing a financial position among
agents with potentially different reference risk measures. The problem is
equivalent to computing the infimal convolution of the risk metrics and finding
the so-called optimal allocations. We propose a neural network-based framework
to solve the problem and we prove the convergence of the approximated
inf-convolution, as well as the approximated optimal allocations, to the
corresponding theoretical values. We support our findings with several
numerical experiments.
