Problems of Monotonicity of Some Popular Risk Measures
Loading...
Date
2016
Authors
Advisor
Editor
Journal Title
Journal ISSN
Volume Title
Publisher
Title alternative
Abstract
In the article the author checked the properties of coherent measures of risk for
Expected Value, Expected Shortfall, Maximum Loss (for losses weighted with probability),
Median, Median Absolute Deviation, “Arithmetic Mean of Absolute Deviations from Median”,
Quantiles, Cumulative Distribution Function and Mid-Range in connection with the last
financial crisis. Methodology of the research – mathematical proving and theoretical analysis.
Results. The survey shows that the above functions are not coherent measures of risk
with some definition of stochastic order and in many cases not measures of risk in terms of
the axiomatic definition. The paper shows also that the lemma used in the literature to prove
monotonicity of Expected Shortfall is not truth and we will prove the lemma with the opposite
relation. Value of the paper – Mathematical proofs in the field of risk measurement.
Showing some problems with monotonicity of risk measures. Contradicting the lemma of
monotonicity of Expected Shortfall. Own definition of first degree stochastic order.
Description
Sponsor
Keywords
measures of Risk, Expected Shotrfall, Expected Value, coherence
Citation
Ekonometria 2(56), 2016, s. 108-122.