Prediction of quantiles at extreme tails is interest in numerous applications. Extreme value modelling provides various competing predictors for this point prediction problem. A common method assessment a set to evaluate their predictive performance given situation. However, due the nature inference problem, it can be possible that predicted are not seen historical records, particularly when sa...

Risk contributions of portfolios form an indispensable part risk adjusted performance measurement. The contribution a portfolio, e.g., in the Euler or Aumann-Shapley framework, is given by partial derivatives measure applied to portfolio return direction asset weights. For measures that are not positively homogeneous degree 1, however, known capital allocation principles do apply. We study clas...

For simulation output the estimation of several quantiles usually provides a deeper insight than mean value analysis. So far, quantile estimation has usually been applied to show the long run behaviour of a system. In this paper we describe a method to depict several quantiles over simulation time to show the transient behaviour. This method is based on independent replications and its capabili...

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We provide a list of functional equations that characterize quantile functions for collections of bounded and measurable functions. Our central axiom is ordinal covariance. When a probability measure is exogeneously given, we characterize quantiles with respect to that measure through monotonicity with respect to stochastic dominance. When none is given, we characterize those functions which ar...

Several types of weighted-automata models and formalisms to specify and verify constraints on accumulated weights have been studied in the past. The lack of monotonicity for weight functions with positive and negative values as well as for ratios of the accumulated values of non-negative weight functions renders many verification problems to be undecidable or computationally hard. Our contribut...