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We consider a class of L\'evy-driven stochastic differential equations (SDEs)with McKean-Vlasov (MK-V) interaction in the drift coefficient. It is assumedthat the coefficient is bounded, affine in the state variable, and onlymeasurable in the law of the solution. We study the equivalent functionalfixed-point equation for the unknown time-dependent coefficients of theassociated Markovian SDE. By proving a contraction property for the functionalmap in a suitable normed space, we infer existence and uniqueness results forthe MK-V SDE, and derive a discretized Picard iteration scheme thatapproximates the law of the solution through its characteristic function.Numerical illustrations show the effectiveness of our method, which appears tobe appropriate to handle the multi-dimensional setting.

A Fourier-based Picard-iteration approach for a class of McKean-Vlasov SDEs with L\'evy jumps