Gerber and Shiu (1997) have studied the joint density of the time of ruin, the surplus immediately before ruin, and the deficit at ruin in the classical model of collective risk theory. More recently, their results have been generalised for risk models where the interarrival density for claims is nonexponential, but belongs to the Erlang family. Here we obtain generalisations of the Gerber–Shiu...

The key-leakage-storage capacity regions for a hidden identifier’s noisy measurements at two terminals of a secrecy system are derived. The capacity regions of binary sources with multiple measurements are obtained by applying Mrs. Gerber’s lemma twice in different directions to a Markov chain to show gains in privacy-leakage as compared to assuming a noise-free identifier at the encoder.

The Satisfactory Partition problem asks for deciding if a given graph has a partition of its vertex set into two nonempty parts such that each vertex has at least as many neighbors in its part as in the other part. This problem was introduced by Gerber and Kobler [EJOR, 125 (2000), 283–291] and studied further by other authors. In this paper we first review some applications and related problem...

The defective renewal equation satisfied by the Gerber-Shiu discounted penalty function in the renewal risk model with arbitrary interclaim times is analyzed. The ladder height distribution is shown to be a mixture of residual lifetime claim severity distributions, which results in an invariance property satisfied by a large class of claim amount models. In particular, when claims are exponenti...

Stefan Weber, Brett Bell, Nicolas Gerber, Tom Williamson ARTORG Center University of Bern Bern, Switzerland Peter Brett, Xinli Du Brunel Institute for Bioengineering Brunel University London, UK Marco Caversaccio Department of ENT, Head and Neck Surgery Bern University Hospital Bern, Switzerland David Proops, Chris Coulson, Andrew Reid Department of Otolaryngology Queen Elizabeth Hospital Birmi...