A distortion risk measure used in finance and insurance is defined as the expected value of potential loss under a scenario probability measure. In this paper, the tail distortion risk measure is introduced to assess tail risks of excess losses modeled by the right tails of loss distributions. The asymptotic linear relation between tail distortion and Value-at-Risk is derived for heavy tailed l...

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 purpose of this study is estimation of daily Value at Risk (VaR) for total index of Tehran Stock Exchange using parametric, nonparametric and semi-parametric approaches. Conditional and unconditional coverage backtesting are used for evaluating the accuracy of calculated VaR and also to compare the performance of mentioned approaches. In most cases, based on backtesting statistics Results, ...

Real-life decisions are usually made in the state of uncertainty or risk. In this article we present the risk measuring techniques value at risk (VaR) and tail value at risk (TVaR) under uncertainty. Firstly, we introduce the VaR concept of uncertain variable based on uncertainty theory and examine its fundamental properties. Then, the TVaR concept is evolved and some fundamental properties of ...

This paper develops a new test to evaluate Value at Risk (VaR) forecasts. VaR is a standard risk measure widely utilized by financial institutions and regulators, yet estimating VaR is a challenging problem, and popular VaR forecast relies on unrealistic assumptions. Hence, assessing the performance of VaR is of great importance. We propose the geometric-VaR test which utilizes the duration bet...