Stochastic Orders and Risk Measures: Consistency and Bounds

By Nicole Bäuerle, Alfred Müller. 2006

153 citations recorded by the source corpus.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/3b455ca163a667aa9fd33f638dfd53c1802412e7

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Citations in the corpus

Generalized Quantiles as Risk Measures (2014, result): “…(2012) showed by means of order theoretic comparative static techniques that expectiles with α ≥ 1 2 are the only generalized quantiles (in the symmetric Φ1 = Φ2 case) that are isotonic with respect to the increasing convex order, in accordance with the results of Bäuerle and Müller (2006).”
Risk aggregation with dependence uncertainty (2014, methodology): “However, when the dependence structure is unspecified, ρ(S) can take a range of possible values, which can then be interpreted as a measure of model uncertainty (Cont (2006)) with the absence of information on dependence. The assessment of aggregate risks S with given marginal distributions and part”
On comonotonicity of Pareto optimal risk sharing (2008, background): “Since all law-invariant convex risk measures are consistent with the convex order (see e.g. Bäuerle and Müller (2006)) it follows that a Pareto-optimal risk allocation is necessarily comonotone.”
Actuarial Theory for Dependent Risks: Measures, Orders and Models (2005, background): “The supermodular and symmetric supermodular orders have been cursorily studied in the applied probability literature; standard references include Joe (1990), Meester and Shanthikumar (1993), Szekli, Disney and Hur (1994), Shaked and Shanthikumar (1997), Bäuerle (1997), Bäuerle and Müller (1998), Mül”
TVaR-based capital allocation with copulas (2009, unknown): “From B¨auerle and M¨uller (2006), it follows that for (cid:20) ∈ (0 ; 1) :”
Consistent risk measures for portfolio vectors (2006, unknown): “2 Remark 3.11 In the one-dimensional case the convex ordering result of Theorem 3.10 has been proved as consequence of the Kusuoka representation result for convex risk measures in Föllmer and Schied (2004, Corollary 4.59) and in a direct way in a recent paper in Bäuerle and Müller (2005).”
Optimal risk sharing under distorted probabilities (2008, background): “On the other hand, Bäuerle and Müller [5] show that any law-invariant convex risk measure, subject to a mild continuity requirement, is consistent with the convex order ≤cx.”
Risk measurement with equivalent utility principles (2006, background): “Coherent risk measures satisfying the objectivity requirement have been studied by Kusuoka (2001); see also Inoue (2003) and B̈auerle & Müller (2006) for an extension to unbounded random variables.”