Two main axiomatically based risk measures are the coherent risk measure, which assumes subadditivity for random variables, and the insurance risk measure, which assumes additivity for comonotonic random variables. We propose a new, data based, risk measure, called natural risk statistic, that is characterized by a new set of axioms. The new axioms only require subadditivity for comonotonic ran...

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 ...

Consider a dynamic decision making model under risk with a fixed planning horizon, namely the dynamic capacity control model. The model describes a firm, operating in a monopolistic setting and selling a range of products consuming a single resource. Demand for each product is time-dependent and modeled by a random variable. The firm controls the revenue stream by allowing or denying customer r...

Management of operational risk is of prime importance in riskmanagement for commercial banks, and many theoretical and practical studies of operational risk management have been carried out. Conditional value-at-risk (CVaR) models based on the peak value method of extreme value theory are used here tomeasure operational risk. Loss data for commercial banks are used in an empirical analysis. Tes...

In this paper, we propose a multiscale dependence-based methodology to analyze the dependence structure and to estimate the downside portfolio risk measures in the energy markets. More specifically, under this methodology, we formulate a new bivariate Empirical Mode Decomposition (EMD) copula based approach to analyze and model the multiscale dependence structure in the energy markets. The prop...

The difference between market risk and potential market risk is emphasized and a measure of the latter risk is proposed. Specifically, it is argued that the spectrum of smooth Lyapunov exponents can be utilized in what we call (λ, σ)-analysis, which is a method to monitor the aforementioned risk measures. The reason is that these exponents focus on the stability properties (λ) of the stochastic...

This paper established the ARMA-GJR-AL model of dynamic risk VaR and CVaR measurement. Considering from aspects of the correlation and volatility and residual distribution characteristics, studying the dynamic risk measures of VaR and CVaR based on ARMA-GJR-AL model. Through empirical research, Risk prediction and accuracy of inspection are given of the Shanghai stock market and the New York st...

We propose a new estimator for expected shortfall that uses asymptotic expansions to account for the asymmetry and heavy tails in financial returns. We provide all the necessary formulas for decomposing estimators of value-at-risk and expected shortfall based on asymptotic expansions and show that this new methodology is very useful for analyzing and predicting the risk properties of portfolios...

Deregulation in the power industry drives competition. It also increases the risk of doing business. Therefore it is important to manage and assess the risk. Value at risk (VaR) analysis has been used in financial institutions to evaluate portfolios of assets for some time, but the application of the approach in the power industry has not been established. The VaR of serving customer demand usi...

Everyone who measures the market risk using the Value at Risk (VaR) approach should test if the assumed model is correct. This procedure is called backtesting. There are many different tests available, but usually risk managers are not concerned about their power. The aim of this paper is to analyze some chosen backtesting methods focusing on the problem of power of the tests and limited data s...