2015/03/30 by Chuancun Yin, Dan Zhu, Yin, Chuancun +1
Decision Sciences · Economics, Econometrics and Finance · #FOS: Economics and business #Financial Risk and Volatility Modeling #Insurance and Financial Risk Management #Risk Management (q-fin.RM) #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.1503.08586
openalex publication_date 2015/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Distortion risk measures are extensively used in finance and insurance applications because of their appealing properties. We present three methods to construct new class of distortion functions and measures. The approach involves the composting methods, the mixing methods and the approach that based on the theory of copula. Subadditivity is an important property when aggregating risks in order to preserve the benefits of diversification. However, Value at risk (VaR), as the most well-known example of distortion risk measure is not always globally subadditive, except of elliptically distributed risks. In this paper, instead of study subadditivity we investigate the tail subadditivity for VaR and other distortion risk measures. In particular, we demonstrate that VaR is tail subadditive for the case where the support of risk is bounded. Various examples are also presented to illustrate the results.