Axiomatic extension of risk measurement

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