Coherent Risk Measures and Linear Programming

Abstract

In recent years, the need for risk measures in highly complex systems, brought a general reconsideration about what features a sound definition of risk should satisfy. Most of the time, the measure of risk must be applied to many different situations, for example the numbers involved are used to compare and to control portfolio investments, as well as trading activities of a department, the exposure to default risk of a class of debts, and so on. It is a natural requirement that those numbers can be compared. But it is necessary that the definition of the risk measure satisfies some mathematical properties, that are given in the form of axioms. This idea forms the core of the theory of coherent risk measures, that was put forward by four scholars in a recent work, [1].