  This paper establishes a verification theorem for impulse control problems
involving conditional McKean-Vlasov jump diffusions. We obtain a Markovian
system by combining the state equation of the problem with the stochastic
Fokker-Planck equation for the conditional probability law of the state. We
derive sufficient variational inequalities for a function to be the value
function of the impulse control problem, and for an impulse control to be the
optimal control. We illustrate our results by applying them to the study of an
optimal stream of dividends under transaction costs. We obtain the solution
explicitly by finding a function and an associated impulse control which
satisfy the verification theorem.
