We consider the Sparre Andersen risk process with interclaim times that belong to the class of distributions with rational Laplace transform. We construct error bounds for the ruin probability based on the Pollaczek-Khintchine formula, and develop an efficient algorithm to approximate the ruin...

In this paper we present an evaluation framework for predictions of binary events in probabilistic electricity price forecasting. It employs the MSE-equivalent QPS together with the DM test and allows for further insights about deficiencies of the considered models. Additionally, techniques from...

Determining distributions of the functions of random variables is one of the most important problems in statistics and applied mathematics because distributions of functions have wide range of applications in numerous areas in economics, finance, risk management, science, and others. However,...

RESTART is a widely applicable accelerated simulation technique that allows the evaluation of extremely low probabilities. In this method a number of retrials (or paths) are made when the process reaches certain thresholds of a function of the system state, called the importance function. In...

In this work, we discuss completeness for the lattice orders of first and second order stochastic dominance. The main results state that, both, first and second order stochastic dominance induce Dedekind super complete lattices, i.e. lattices in which every bounded nonempty subset has a...

Travel times for simple trips and cycles are analyzed for a storage/retrieval machine working in a one-dimensional or two-dimensional zone with taxicab geometry. A semi-random trip is defined as one-way travel from a known to a random location or vice versa. A random trip is defined as one-way...