We examine discounted penalties at ruin for surplus dynamics driven by a general spectrally negative Lévy process; the natural class of stochastic processes which contains many examples of risk processes which have already been considered in the existing literature. Following from the important contributions of Zhou (2005) we provide an explicit characterization of a generalized version of the ...

6 7 David Amblas, Thomas P. Gerber, Miquel Canals, Lincoln F. Pratson, Roger 8 Urgeles, Galderic Lastras, Antoni M. Calafat 9 10 GRC Geociències Marines, Facultat de Geologia, Universitat de Barcelona, E-08028 Barcelona, Spain 11 Department of Geology, University at Buffalo, NY 14260 Buffalo, USA 12 Division of Earth & Ocean Sciences, Duke University, NC 27708 Durham, USA 13 Dept. Geologia Mari...

D. A. Lidar,* D. Thirumalai, R. Elber, and R. B. Gerber Department of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel Department of Physical Chemistry and The Fritz Haber Center for Molecular Dynamics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel Department of Chemistry and Biochemistry, Institute for Physical Science and Technology, University of Maryland, C...

Galina Chaban,‡ R. Benny Gerber,*,‡ Mikhail V. Korolkov,§,| Jo1rn Manz,| Masha Y. Niv,‡ and Burkhard Schmidt⊥ Fritz-Haber-Center for Molecular Dynamics, Hebrew UniVersity, GiVat Ram, 91904 Jerusalem, Israel, B. I. StepanoV Institute of Physics, Academy of Sciences of Belarus, Skaryna AVe. 70, 220602 Minsk, Republic of Belarus, Institut für Chemie, Freie UniVersität Berlin, Takustrasse 3, D-1419...

Abstract—In this paper, we consider a risk model involving two independent classes of insurance risks and random premium income. We assume that the premium income process is a Poisson Process, and the claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. Both of the GerberShiu functions with zero initial surplus and the probability generating function...

Despite the wealth of metagenomic sequencing data, the functions of most bacterial genes from the mammalian microbiota have remained poorly understood. In their recent study (Yaung et al 2015), Wang, Gerber, and colleagues present a platform which allows functional mining of bacterial genomes for genes that contribute to fitness in vivo and holds great potential for forward engineering microbes...

We introduce an algebraic operator framework to study discounted penalty functions in renewal risk models. For inter-arrival and claim size distributions with rational Laplace transform, the usual integral equation is transformed into a boundary value problem, which is solved by symbolic techniques. The factorization of the differential operator can be lifted to the level of boundary value prob...