Coherent allocation of risk capital

By Michel Denault. 2001

440 citations recorded by the source corpus.

Subfields: Economics and Econometrics, General Decision Sciences, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/626a1864f66cf53242ec3dc238ed056d50e8bc6a

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Citations in the corpus

Risk Capital Allocation and Cooperative Pricing of Insurance Liabilities (2003, neutral): “This type of risk measures have been axiomatically defined in the context of insurance pricing by Denneberg (1990) and Wang et al. (1997). They are termed distortion principles, since the non-linear function g ‘distorts’ the physical probability measure P0.”
Weighted Risk Capital Allocations (2008, positive): “At the moment we only briefly note that while desirable properties of risk measures have been extensively studied in the literature for a long time (see, e.g., Goovaerts et al. (1984), Artzner et al. (1999), Denuit et al. (2005), Dhaene et al. (2006); and references therein), properties of allocatio”
Weighted Pricing Functionals With Applications to Insurance (2009, background): “…is less voluminous, although it has been actively developing during the last decade, especially in the context of allocations (see, e.g., Denault 2001; Hesselager and Andersson 2002; Dhaene et al. 2003; Goovaerts et al. 2003; Venter 2004; Kalkbrener 2005; Venter et al. 2006; Kim 2007;…”
Integrated risk modelling (2004, background): “Readers interested in this issue may refer Ward and Lee (2002) and Denault (2001).”
Asset Allocation with Conditional Value-at-Risk Budgets (2013, positive): “Using game theory, Denault (2001) has shown that the only satisfactory risk allocation principle is to measure the risk contribution as the weight of the position in the portfolio times the partial derivative of the portfolio risk Rw with respect to that weight: C.i/Rw D w.i/ @Rw @w.i/ : (2.1) The…”
On the Impossibility of Fair Risk Allocation (2010, background): “Denault (2001) considers the original axiomatization of the Shapley value by Shapley (1953), and concludes that there is no allocation which satisfies Core Compatibility, Equal Treatment Property, Dummy Player Property (a riskless division should be allocated its stand-alone risk) and Additivity…”
Optimal Capital Allocation Principles (2005, neutral): “Keywords: Capital allocation; risk measure; comonotonicity; Euler allocation; default option; Lloyd’s of London.”
Multivariate distribution defined with Farlie–Gumbel–Morgenstern copula and mixed Erlang marginals: Aggregation and capital allocation (2013, positive): “The FGM copula is a perturbation of the product copula and, as mentioned in Nelsen (2006), is a first order approximation to the Ali Mikhail Haq, Frank and Placket copulas.”
Risk factor contributions in portfolio credit risk models (2010, background): “…contributions, e.g. Kalkbrener (2005), as well as the interpretation of the Euler allocation rule in terms of the theory of cooperative games, e.g. Denault (2001) or 4 This equation relies on our assumption that loss-given-default adjusted expores are constant. su 6 The Hoeffding decomposition…”
On the optimal risk allocation problem (2006, background): “…(2002a, 2002b, 2003, 2004, 2005), Dana and Scarsini (2005), Chateauneuf, Dana, and Tallon (2000), Gerber (1979), Landsberger and Meilijson (1994), Denault (2001), Dana and Meilijson (2003), Heath and Ku (2004), Carlier and Dana (2003), Burgert and Rüschendorf (2005), Jouini, Schachermayer, and…”
Measuring and Managing Credit Risk (2004, background): “This approach to incomplete contracts and contingent allocation of control rights has been developed by Grossman and Hart (1982), Holmström and Tirole (1989), Aghion and Bolton (1992), Dewatripont and Tirole (1994), and Hart and Moore (1998). 25. Aghion and Bolton (1992) observe that debt is not the”
Wang’s capital allocation formula for elliptically contoured distributions (2003, background): “Some straightforward calculation similar to the proof of Lemma (6) yields the results: E ¡ ZeλZ ¢ = exp µ λµZ + λ2σ2Z 2 ¶ · (µ+ λσ2Z) E ¡ Xie λZ ¢ = exp µ λµZ + λ2σ2Z 2 ¶ · (µi + λσi,Z) where µZ and µi are the mean losses of the aggregate Z and the i th line of business respectively, and σ2Z = Pn i,”
Dynamic capital allocation with distortion risk measures (2004, neutral): “expectations with respect to the additive probability measures in P) see Denneberg (2000). Related approaches can be found in Walley (1991), who studied the problem in the context of quasi-Bayesian statistics and decision theory, and Lehrer (1996), who proposed a geometrical construction.”