AbstractsMathematics

Mathematics of Risk Measures. And the measures of the Basel Committee.

by M.F. van Rijn




Institution: Universiteit Utrecht
Department:
Year: 2015
Keywords: Value-at-Risk, Stressed Value-at-Risk, Expected Shortfall, Expectiles, Risk Measures, Coherent, Elicitable
Record ID: 1248557
Full text PDF: http://dspace.library.uu.nl:8080/handle/1874/307057


Abstract

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.