2022
DOI: 10.1016/j.jbankfin.2021.106315
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Coherent risk measures alone are ineffective in constraining portfolio losses

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Cited by 4 publications
(6 citation statements)
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“…The ineffectiveness of static risk constraints based on the coherent risk measure ρ is shown to be equivalent to the existence of a ρ-arbitrage. 1 Again, the emphasis for us, in this paper, is that also in Armstrong and Brigo (2018) and Armstrong and Brigo (2022) the risk constraints are static and that the situation becomes very different with dynamic risk constraints.…”
Section: Introductionmentioning
confidence: 94%
See 2 more Smart Citations
“…The ineffectiveness of static risk constraints based on the coherent risk measure ρ is shown to be equivalent to the existence of a ρ-arbitrage. 1 Again, the emphasis for us, in this paper, is that also in Armstrong and Brigo (2018) and Armstrong and Brigo (2022) the risk constraints are static and that the situation becomes very different with dynamic risk constraints.…”
Section: Introductionmentioning
confidence: 94%
“…7 An interesting question is what will happen if (B.6) does not hold such that −ES α ( f , S, t) ≥ P( f , S, t). Using the terminology of Armstrong and Brigo (2022), the call option in this case exhibits the so-called "ρ-arbitrage" which refers to the existence of a payoff with non-positive Fig. 5 The values of P( f , S, t) and −ES α ( f , S, t) for f being the call option payoff with strike K .…”
Section: Proof Of Propositionmentioning
confidence: 99%
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“…Let l be a loss function and assume l| R − ≡ 0. Then the following are equivalent: 5 One can check that the result (including Proposition D.4) extends to functions l : R → R that are nondecreasing, convex, and satisfy l(0) = 0 as well as limx→∞ l(x) = ∞ (which is weaker than l(x) ≥ x for all x ∈ R). (a) The market (S 0 , S) does not admit SR l -arbitrage if and only if there exists Z ∈ P such that a l + ε < kZ < b l − ε P-a.s. for some k, ε > 0.…”
Section: Shortfall Risk Measuresmentioning
confidence: 99%
“…These phenomena are referred to as ρ-arbitrage (a generalisation of arbitrage of the first kind) and strong ρ-arbitrage (a generalisation of arbitrage of the second kind), respectively. Both concepts have been studied extensively in Herdegen and Khan [34] from a theoretical perspective; the practical relevance of ρ-arbitrage has been discussed by Armstrong and Brigo in [6] and [5]. In particular, [34,Theorem 3.23] implies that regulators cannot exclude (strong) ρ-arbitrage a priori when imposing a positively homogeneous (monotone and cash-invariant) risk measure -unless ρ is as conservative as the worst-case risk measure.…”
Section: Introductionmentioning
confidence: 99%