Let {(Xi,Yi): i=…,-1,0,1,…} be a doubly infinite renewal-reward process, where {Xi: i=…-1,0,1,…} is an independent identically distributed sequence of renewal cycle lengths and Yi=g(Xi-q,Xi-q+1,…,Xi) is the lump reward earned at the end of the ith renewal cycle, with some function g: ℜq+1 → ℜ. Starting with the first renewal cycle (of duration Xi) at the time origin, let C(t) denote the expected cumulative reward earned in (0,t]. In this paper, an asymptotic representation for C of the form C(t)=ξt+η+o(1), t → ∞, is derived. An application of this result in single item replacement modelling is discussed.
