A General Bound for the Net Premium of the Largest Claims Reinsurance Covers

Abstract

For a general class of reinsurance treaties the author gives an upper bound for the net premium. This result can be seen as the counterpart to a premium bound for the classical stop-loss reinsurance cover (see Bowers, 1969). For some special cases some preliminary work can be found in Kremer (1983).

Largest Claims Reinsurance Premiums under Possible Claims Dependence

“…A paper by Heilmann (1986) treats with the stoploss cover under relaxation of the independence assumption. Some results in Kremer (1988) hold also in case of dependence of the claims sizes for (generalized) largest claims covers.…”

“…which is even more handy than (4.1). When one takes a closer look into Kremer (1988), one can find out that the theorem 1 there holds true also in case that (A.3) is not necessarily given. This means that the there given premium rate bound:…”

A Note on the Net Premium for a Generalized Largest Claims Reinsurance Cover

“…where a,-, / > 1, are real constants. This reinsurance treaty is defined as the generalized largest claims cover (KREMER 1988b). We get for a; = «2 = • • • = a p = 1, cij = 0 V / > p the so called LCR(/?)…”

The asymptotic efficiency of largest claims reinsurance treaties

“…Nearly nothing is known on the goodness of the largest claims reinsurance treaty or of some of its interesting generalizations, which are defined e.g. in KREMER (1986aKREMER ( ), (1988a. Some remarks on certain dependencies between the largest claims and excess-of-loss treaty can be found in BERLINER (1972).…”