  We present and establish large deviations principles for general multivariate
renewal-reward processes associated with a classical discrete-time renewal
process. A renewal-reward process describes a cumulative reward over time,
supposing that a broad-sense multivariate reward is obtained at each occurrence
of the event that is renewed under the renewal process. We consider both the
standard model and a constrained model that is constructed conditioning on the
event that one of the renewals occurs at a predetermined time. With a different
interpretation of the time coordinate, the constrained renewal model includes
several important models of statistical mechanics, such as the model of polymer
pinning, the Poland-Scheraga model of DNA denaturation, the
Wako-Sait\^o-Mu\~noz-Eaton model of protein folding, and the Tokar-Dreyss\'e
model of strained epitaxy. We attack the problem of large deviations in
constrained renewal models by an argument based on convexity and
super-additivity. Then, we transfer results to standard renewal processes by
resorting to conditioning. In the context of constrained renewal models, we
also propose an explicit application of the general theory to deterministic
rewards that grow no faster than the time elapsed between two successive
occurrences of the renewed event. This type of rewards codifies the extensive
variables of statistical mechanics.
