Axiomatic Extension of Risk Measurement

Abstract

In the article the author introduce and prove the additional axiom of measure of risk. She checks, by the method of mathematical proving, which from the well-known functions of risk fulfill this additional axiom. This proofs will be conducted for functions such as: Value at Risk, Expected Shortfall, Median, Abso-lute Median Deviation, Maximum , Maximum Loss, Half Range, and Arithmetic Average. In other words the purpose of the paper is studying which from the above functions fulfill the additional axiom of measure of risk, which can enrich the Arzner’s and other axioms. This axiom is not a consequence of the Arzner’s and other axioms. Furthermore the author researches mathematically if mentioned func-tions of risk retain properties after replacing the stochastic order with partial order. At the end the author presents the new measure of risk which fulfill all the axioms of measure of risk and the additional axiom.