Abstract
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.
Highlights
A risk measure ρ is a mapping from the set of random variables, standing for risky portfolios of assets and/or liabilities, to the real line R
We investigate the tail subadditivity for VaR and other distortion risk measures
Distortion risk measures satisfy a set of properties including positive homogeneity, translation invariance and monotonicity
Summary
A risk measure ρ is a mapping from the set of random variables , standing for risky portfolios of assets and/or liabilities, to the real line R. Positive values of elements of will be considered to represent losses, while negative values will represent gains. Distortion risk measures are a particular and most important family of risk measures that have been extensively used in finance and insurance as capital requirement and principles of premium calculation for the regulator and supervisor. Several popular risk measures belong to the family of distortion risk measures. The value-at-risk (VaR), the tail value-at-risk (TVaR) and the Wang distortion measure. Distortion risk measures satisfy a set of properties including positive homogeneity, translation invariance and monotonicity. When the associated distortion function is concave, the distortion risk measure is subadditive (Denneberg, 1994; Wang & Dhaene, 1998).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
