OPTIMAL IMPULSE CONTROL WHEN CONTROL ACTIONS HAVE RANDOM CONSEQUENCES

We consider a generalised impulse control model for controlling a proc ess governed by a stochastic differential equation. The controller can only choose a parameter of the probability distribution of the conseq uence of his control action which is therefore random. We state optima lity results relating the value function to quasi-variational inequali ties and a formal optimal stopping problem. We also remark that the va lue function is a viscosity solution of the quasivariational inequalit ies which could lead to developments and convergence proofs of numeric al schemes. Further, we give some explicit examples and an application in financial mathematics, the optimal control of the exchange rate.