Tail Conditional Expectations for Elliptical Distributions

By Zinoviy Landsman, Emiliano A. Valdez. 2003

398 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/06efa1b1a3d904f7a7f95c2bf7c0ff2476e23727

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Citations in the corpus

Estimating conditional tail expectation with actuarial applications in view (2008, methodology): “The ACC was introduced by Shalit and Yitzhaki (1994). For subsequent developments in the area we refer, for example, to Mayshar and Yitzhaki (1995), Chow (2001), Seiler (2001), Shalit and Yitzhaki (2003), Schechtman and Yitzhaki (2004), and references therein.”
TVaR-based capital allocation for multivariate compound distributions with positive continuous claim amounts (2012, background): “…some specific multivariate distributions for (X1, . . . , Xn): multivariate normal distribution (Panjer, 2002), multivariate elliptical distribution (Landsman and Valdez, 2003 and Dhaene et al., 2008), multivariate gamma distribution (Furman and Landsman, 2005), multivariate Tweedie distribution…”
Economic Capital and the Aggregation of Risks Using Copulas (2009, background): “Two further references for elliptical distributions are Landsman and Valdez (2003) and Valdez and Chernih (2003).”
Non‐parametric Estimation of Extreme Risk Measures from Conditional Heavy‐tailed Distributions (2014, background): “The CTE is defined as the expected loss given that the loss lies above the upper ˛-quantile of the loss distribution.”
Tail Conditional Expectations for Exponential Dispersion Models (2005, background): “…− ) ´ 1− Φ ³√ ( − ) ´ Reparameterizing back to and "2, we find from (15) that the TCE for the Normal distribution gives ( ) = + 1 √ & ³√ ( − ) ´ 1− Φ ³√ ( − ) ´ = + (1 ")& [( − ) "] 1− Φ [( − ) "] " 2 (19) This gives the same formula as that derived in Panjer (2002) and Landsman and Valdez (2003).”
Estimation of the marginal expected shortfall: the mean when a related variable is extreme (2012, background): “For example, Landsman and Valdez (2003) and Kostadinov (2006) deal with elliptical distributions with heavy-tailed marginals.”
A New Approach to Assessing Model Risk in High Dimensions (2015, neutral): “It is only when the level of the upper bound is equal to ∑d i=1 TVaRp (Xi) , which can be computed explicitly (see Landsman and Valdez (2003)).”
Tail Conditional Variance for Elliptically Contoured Distributions (2004, methodology): “0 xgn(x)dx <∞ (15) guarantees gn(x) to be density generator (Fang, et al.”
Weighted Risk Capital Allocations (2008, positive): “For results, which are mainly related to TCEtype capital allocations, we refer to Hurlimann (2001), Panjer and Jing (2001), Panjer (2002), Landsman and Valdez (2003) , Cai and Li (2005), Furman and Landsman (2005, 2007), Chiragiev and Landsman (2007), Vernic (2008) and Dhaene et al. (2008a,b), and ”
Asymptotics for Risk Capital Allocations Based on Conditional Tail Expectation (2011, neutral): “To emphasize the point, we refer the reader to Panjer and Jia (2001), Landsman and Valdez (2003), Valdez and Chernih (2003), Cai and Li (2005), Furman and Landsman (2005, 2006, 2008), Chiragiev and Landsman (2007), Vernic (2006, 2011) and Dhaene et al. (2008) for analytic expressions for (1.1)…”
Optimal Capital Allocation Principles (2005, positive): “Dhaene et al. (2008) derive the results of Landsman and Valdez (2003) in a rather more straightforward manner and apply these to sums that involve normal as well as lognormal risks.”
Tail Risk of Multivariate Regular Variation (2011, background): “The risk allocation/decomposition with TCE for elliptically distributed loss vectors can be found in [24].”
Multivariate Pareto portfolios: TCE-based capital allocation and divided differences (2007, background): “Although rapid growth is observed in the literature in deriving TCE-based allocations (multivariate normal family was developed by Panjer ( 2002 ), and his results were generalized by Landsman & Valdez ( 2003 ) for the essentially larger class of elliptical distributions, Cai & Tan ( 2005 ) for mult”
Asymptotic Analysis of Multivariate Tail Conditional Expectations (2012, methodology): “…3 we discuss the asymptotic properties of TCEs for multivariate elliptical distributions and, in particular, compare the tail estimates of TCEs obtained from our asymptotic approach and ones derived from the exact TCE formulas obtained in Landsman and Valdez (2003) for elliptical distributions.”