Different kinds of renewal equations repeatedly arise in connectionwith renewal risk models and variations. It is often appropriate toutilize bounds instead of the general solution to the renewalequation due to the inherent complexity. For this reason, as a firstapproach to construction of bounds we employ a general Lundberg-typemethodology. Second, we focus specifically on exponential boundswhich have the advantageous feature of being closely connected tothe asymptotic behavior (for large values of the argument) of therenewal function. Finally, the last section of this paper includesseveral applications to risk theory quantities.
