Bounds based on reliability classifications

Abstract

The general bounds given in theorems 4.2.1 and 4.3.1 require minimizing or maximizing the function c(x, z) in (4.2.4), which may be awkward to evaluate. Simpler bounds are thus derived in the corollaries of these theorems and they are applicable for an arbitrary individual claim amount df F(y). In this chapter we employ the results of chapter 4 with additional assumptions about the df F(y). By taking advantage of reliability properties of F(y), refinements of these bounds on the tail of the aggregate claims distribution are obtainable. Naturally, these refined bounds are sharper than those given in the corollaries and but still simple enough to use. The next section deals with first order assumptions about the df F(y), by which we mean assumptions about the failure rate and the distribution function of the residual lifetime associated with F(y). The following section deals with assumptions involving the equilibrium df F₁(y).