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This paper establishes a verification theorem for impulse control problemsinvolving conditional McKean-Vlasov jump diffusions. We obtain a Markoviansystem by combining the state equation of the problem with the stochasticFokker-Planck equation for the conditional probability law of the state. Wederive sufficient variational inequalities for a function to be the valuefunction of the impulse control problem, and for an impulse control to be theoptimal control. We illustrate our results by applying them to the study of anoptimal stream of dividends under transaction costs. We obtain the solutionexplicitly by finding a function and an associated impulse control whichsatisfy the verification theorem.

Impulse control of conditional McKean-Vlasov jump diffusions