Starting with a time-0 coherent risk measure defined for “value processes”, we also define risk measurement processes. Two other constructions of measurement processes are given in terms of sets of test probabilities. These latter constructions are identical and are related to the former construction when the sets fulfill a stability condition also met in multiperiod treatment of ambiguity as i...

Evaluating risk measures, premiums, and capital allocation based on dependent multi-losses is a notoriously difficult task. In this paper, we demonstrate how this can be successfully accomplished when losses follow the multivariate Pareto distribution of the second kind, which is an attractive model for multi-losses whose dependence and tail heaviness are influenced by a heavy-tailed background...

The class of all law invariant, convex risk measures for portfolio vectors is characterized. The building blocks of this class are shown to be formed by the maximal correlation risk measures. We introduce some classes of multivariate distortion risk measures and relate them to multivariate quantile functionals and to an extension of the average value at risk measure.

Weather derivatives enable energy companies to protect themselves against weather risk. Weather ensemble predictions are generated from atmospheric models and consist of multiple future scenarios for a weather variable. They can be used to forecast the density of the payoff from a weather derivative. The mean of the density is the fair price of the derivative, and the distribution about the mea...

Value at risk is an important measure of extent to which a given portfolio is subject to different kinds of risk present in financial markets. Considerable amount of research was dedicated during recent years to development of acceptable methods for evaluation of this risk measure. In this paper we go beyond estimation of value at risk and address the following questions. Suppose that a boundar...

Understanding the occurrence and nature of violence in the military entails appreciating military culture, the sociology and demographics of its personnel, military training, combat experiences, and injuries and illnesses that veterans suffer. The military is grounded in the principles and practice of conducting violent operations, and the psychology of violence fundamentally anchors its profes...

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