Problems of monotonicity of some popular risk measures

• Authors: Khemissi Eliza

Title variants

PL

Problemy monotoniczności pewnych popularnych miar ryzyka

• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

measures of risk; Expected Shortfall; Expected Value; Maximum Loss; coherence

• Publisher: Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
• Journal: Econometrics. Ekonometria. Advances in Applied Data Analytics
• Year: 2016
• Issue: 2 (52)
• Pages: 108-122

Contributors

author

Khemissi Eliza

References

• Acerbi C., 2002, Spectral Measures of Risk: a Coherent Representation of Sub- jective Risk Aversion, Abaxbank, Corso Monforte 34, 20122 Milano (Italy), DOI: 10.1016/S0378-4266(02)00281-9.
• Acerbi C., Tasche D., 2002, On the coherence of expected shortfall, Journal of Banking & Finance, Volume 26, Issue 7, July, pp. 1487–1503.
• Artzner Ph., Delbaen F., Eber J.M., Heath D., 1997, Thinking coherently, Risk, 10, November, 68-71.1997, DOI: 10.1201/b15055-1.
• Artzner Ph., Delbaen F., Eber J.M., Heath D., 1998, Coherent Measures of Risk https://people.math.ethz.ch/~delbaen/ftp/preprints/CoherentMFdf.
• Buszkowska E., 2015, O fundamentach pomiaru ryzyka, Zeszyty Naukowe: Finanse, Rynki Finansowe Ubezpieczenia, Szczecin.
• Czernik T., 2003, Maksymalna strata jako miara ryzyka, Prace Naukowe Akademii Ekonomicznej w Katowicach.
• Ferguson Ch.H., 2010, Inside Job, Documentary film, USA. Jajuga K., 2007, Zarządzanie ryzykiem, Wydawnictwo Naukowe PWN SA, Warszawa.
• Staniec I., Zawiła-Niedźwiedzki J., 2008, Zarządzanie ryzykiem operacyjnym, Warszawa. Trzpiot G., 2008, O wybranych własnościach miar ryzyka, Badania Operacyjne i Decyzje.
• Uniejewski P., 2004, Koherentne miary ryzyka, Wrocław.