Regensburg 2007 – scientific programme

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AKSOE: Arbeitskreis Physik sozio-ökonomischer Systeme

AKSOE 2: Financial Markets and Risk Management I

AKSOE 2.4: Talk

Monday, March 26, 2007, 11:45–12:15, H8

Measure of risk: has it to be coherent — •Uli Spreitzer and Vladimir Reznik — Dr. Dr. Heissmann GmbH, 65189 Wiesbaden

Artzner et al. [1] postulated, that a measure of risk has to be coherent, i.e.translation invariance, subadditivity, positive homogeneity and monotonicity. Homogenous measures of risk are e.g. tail VaR or lower partial moments [2-3]. The often used VaR is not a homogenous measure of risk.

But a coherent measure means, that there a some assumptions a piori, which habe to be at least be discussed. E.g. the subadditivity of the homogenous means that putting two assembles - e.g. two insurance companies and their contracts - does decrease or at least not increase the risk of the two assembles. But this holds only by making some more postulates on this new larger assemble apriori.

When these postulates can not be fulfilled, a coherent measure of risk gives wrong informations on this new assemble and one should therefore use non coherent measures of risk as e.g. VaR.

[1]P. Artzner et al. Finance 9 (1999)3, 203-228 [2] V. Reznik, U.Spreitzer, talk 28th ICA, 28.5. - 2.6.2006, Paris [3] U. Spreitzer, V. Reznik, On the opt... Physica A (2007)