Decomposing Portfolio Value-at-Risk: A General Analysis

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Conditional Expectation as Quantile Derivative (2001, background): “The primary intention with the present paper is to give a sufficient condition as general as possible on the underlying distribution for the formulae in [9] and [8]) to remain valid.”
ON THE FINANCIAL INTERPRETATION OF RISK CONTRIBUTION: RISK BUDGETS DO ADD UP (2006, background): “First, because VaR is a linear homogeneous function of weights (Litterman, 1996; Hallerbach, 2003), it is mathematically true that”
Expected shortfall and beyond (2002, methodology): “The question of how to compute the partial derivatives in case ρ = VaRα was independently tackled by several authors (Gouriéroux et al., 2000; Hallerbach, 1999; Lemus, 1999; Tasche, 1999).”
AN AXIOMATIC APPROACH TO CAPITAL ALLOCATION (2005, unknown): “Theoretical and practical aspects of different allocation schemes have been analyzed in a number of papers, for instance in Garman (1996, 1997), Hallerbach (1999), Schmock and Straumann (1999), Artzner et al. (1999b), Delbaen (2000), Overbeck (2000), Denault (2001), Tasche (1999, 2002), Fischer…”
Estimation and Decomposition of Downside Risk for Portfolios with Non-Normal Returns (2008, background): “with G 1( ) the quantile function associated to G( ). Comparing ( 16 ) with”