In this chapter we discuss basic concepts which are essential in quantitative riskmanagement. We begin by introducing a mathematical framework for modellingfinancial risk. Following standard practice we use the language of probabilitytheory. In particular, risk is represented by random variables, mapping unforeseenfuture states of the world into values representing profits and losses. Therandom evolution of profits and losses is driven by a set of underlying randomvariables termed risk factors. We give precise formal definitions of these concepts,which help to clarify our analysis later on. Moreover, we discuss a numberof examples from the area of market and credit risk, illustrating how typical riskmanagement problems fit into our framework.

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VaR Methods——Properties of VaR