On exponential functionals for processes with independent increments

In this paper we study exponential integral functionals of semimartingales having independent increment. When the semi-martingale have moreover absolutely continuous characteristics, we derive necessary and sufficient conditions for the existence of the Laplace exponent of the functional and also the sufficient conditions of finiteness of its Mellin transform. We give a recurrent integral equations for this Mellin transform and apply these recurrent formulas to calculate the moments.