On the existence of moments of ladder heights

Let S0S0, Sn=∑k=1nXk, where XkXk, k=1,n¯ are iid random variables. Denote N-=min{n⩾1:Sn⩽0},N+=min{n⩾1:Sn>0}. Necessary and sufficient conditions are found for the existence of the moments of ladder heights SN-SN- and SN+SN+. These conditions are taken into consideration when calculating the moments of ladder heights in the cases EXk>0EXk>0 and EXk<0EXk<0.