This paper aims to examine the factors affecting an insurer's purchasing decisions when considering reinsurance and CAT bond options. In particular, we aim to examine this issue through a constrained optimization model, wherein the insurer seeks to minimize the cost of reinsurance subject to a fixed layer of losses. The solution to the constrained optimization problem will lead to an analysis of several significant factors behind allocation decisions as well as how these factors affect the quantity of traditional reinsurance purchased or CAT bonds issued.