Empirical Estimation of the Haezendonck-Goovaerts Risk

 In this thesis, we describe and study the empirical Haezendonck-Goovaerts (HG) risk measure. First, we introduce the HG risk measure, and provide the mathematical construction of the HG measure. We then show that the HG risk measure is coherent, and describe estimation methods. We perform extensive numerical experiments, and conclude that the optimization methodology of estimating risk with the HG has significant flaws. We find that the empirical method of estimation is a significant improvement over estimation via optimization with respect to both speed and accuracy, and that the empirical method has the behaviours of asymptotic normality and weak convergence. Finally, we perform a case study with a Canadian portfolio, and compare the results to the well-known and well-used risk measure expected shortfall.