Abstract
In recent years, expectation distortion risk measures have been widely used in financial and insurance applications due to their attractive properties. The author introduced two new classes of financial risk measures “VaR raised to the power of t” and “ES raised to the power of t” in his works and also investigated the issue of the belonging of these risk measures to the class of risk measures of expectation distortion, and described the corresponding distortion functions. The aim of this study is to introduce a new concept of variance distortion risk measures, which opens up a significant area for investigating the properties of these risk measures that may be useful in applications. The paper proposes a method of finding new variance distortion risk measures that can be used to acquire risk measures with special properties. As a result of the study, it was found that the class of risk measures of variance distortion includes risk measures that are in a certain way related to “VaR raised to the power of t” and “ES raised to the power of t” measures. The article describes the composite method for constructing new variance distortion functions and corresponding distortion risk measures. This method is used to build a large set of examples of variance distortion risk measures that can be used in assessing certain financial risks of a catastrophic nature. The author concludes that the study of the variance distortion risk measures introduced in this paper can be used both for the development of theoretical risk management methods and in the practice of business risk management in assessing unlikely risks of high catastrophe.
Highlights
The author introduced two new classes of financial risk measures “VaR raised to the power of t” and “ES raised to the power of t” in his works and investigated the issue of the belonging of these risk measures to the class of risk measures of expectation distortion, and described the corresponding distortion functions
The aim of this study is to introduce a new concept of variance distortion risk measures, which opens up a significant area for investigating the properties of these risk measures that may be useful in applications
The paper proposes a method of finding new variance distortion risk measures that can be used to acquire risk measures with special properties
Summary
В работе предложен метод поиска новых мер риска искажения дисперсии, которые можно использовать для приобретения мер риска, обладающих особыми свойствами. В результате исследования выяснилось, что к классу мер риска искажения дисперсии принадлежат меры риска, определенным образом связанные с мерами «VaR в степени t» и «ES в степени t». В работе описан композитный метод построения новых функций искажения дисперсии и соответствующих мер риска искажения. Этот метод использован для построения большого набора примеров мер риска искажения дисперсии, которые могут найти применение при оценке определенных финансовых рисков катастрофической природы. Что исследование введенных в работе мер риска искажения дисперсии может быть полезно как для развития теоретических методов риск-менеджмента, так и в практике риск-менеджмента компаний при оценке маловероятных рисков высокой катастрофичности.
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