An Analysis of the Haezendonck-Goovaerts Risk Measure

The goal of this thesis is to analyse the Haezendonck-Goovaerts (HG) risk measure and see how it compares to other well known and used risk metrics. In particular a focus on Expected Shortfall is presented as the main source of comparison due to the similarities between the two risk measures. The Young Function associated with the HG risk measure that will be k focused on will be of the form ’(t) = t^k. In the case where k = 1, the HG risk measure is equivalent to Expected Shortfall[1], and it is for this reason in this thesis the focus will be on the k = 2 case. An experiment is then run on the risk measures where a model is used on the returns of a portfolio, and see which gives a more conservative result at the same significance level.