Mathematics of Risk Measures. And the measures of the Basel Committee.
Rijn, M.F. van
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Risk measurement within financial institutions remains of the utmost importance in practice. In the last few years it has become evident that a mathematical model should consider two steps of the risk measurement procedure; the estimation of the loss distribution and the construction of a risk measure that summarizes the risk of a position. In 1997 Artzner et all. gave rise to a whole new theory concerning risk measures with their axiomatic approach to coherent risk measures. In my thesis I extend this axiomatic approach to include not only mathematical properties of risk measures but also their statical properties. I will treat two important classes of risk measures and argue that a risk measure should belong to both these classes in order to deal with all aspects of the risk measurement procedure. I will discuss Value-at-Risk, Expected Shortfall en Expectile Value-at-Risk and compare these to the risk measures introduced by the Basel Committee.