title: Risk theory with a nonlinear dividend barrier
abstract: In the framework of classical risk theory we investigate a surplus process in the presence of a nonlinear dividend barrier and derive equations for two characteristics of such a process, the probability of survival and the expected sum of discounted dividend payments. Number-theoretic solution techniques are developed for approximating these quantities and numerical illustrations are given for exponential claim sizes and a parabolic dividend barrier
keyphrases: risk theory nonlinear dividend barrier surplus process probability of survival discounted dividend payments number-theoretic solution numerical illustrations exponential claim sizes parabolic dividend barrier