A note on natural risk statistics

Ahmed, Shabbir; Filipović, Damir; Svindland, Gregor

doi:10.1016/j.orl.2008.06.009

Cited by 27 publications

(23 citation statements)

References 2 publications

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“…It turns out that there is an incompatibility between robustness and coherence for natural risk statistics (see [4]). This fact is documented in [1] and is a consequence of the very characterization of natural risk statistics. As we will see in the last section, coherent risk measures have a representation that give more weight to larger losses and that is at the heart of this incompatibility.…”

Section: Natural Risk Statisticsmentioning

confidence: 98%

“…We notice that if A = R n , then Definition 2.1 is the one in [1] and [9]. If A = l ∞ or c l , then Definition 2.1 is an extended definition of natural risk statistics for infinite data sets.…”

Section: Natural Risk Statisticsmentioning

confidence: 99%

“…The proof can be found in both [1] and [9]. The proof in [1] is more straight-forward than the proof in [9]. Yet, the second one accepts more naturally an extension to the infinite dimension framework.…”

Section: Natural Risk Statisticsmentioning

confidence: 99%

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Risk measures on the space of infinite sequences

Assa

Morales

2010

Math Finan Econ

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Axiomatically based risk measures have been the object of numerous studies and generalizations in recent years. In the literature we find two main schools: coherent risk measures (Artzner, Coherent Measures of Risk. Risk Management: Value at Risk and Beyond, 1998) and insurance risk measures (Wang, Insur Math Econ 21:173-183, 1997). In this note, we set to study yet another extension motivated by a third axiomatically based risk measure that has been recently introduced. In Heyde et al. (Working Paper, Columbia University, 2007), the concept of natural risk statistic is discussed as a data-based risk measure, i.e. as an axiomatic risk measure defined in the space R n . One drawback of these kind of risk measures is their dependence on the space dimension n. In order to circumvent this issue, we propose a way to define a family {ρ n } n=1,2,... of natural risk statistics whose members are defined on R n and related in an appropriate way. This construction requires the generalization of natural risk statistics to the space of infinite sequences l ∞ .

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Section: Natural Risk Statisticsmentioning

confidence: 98%

Section: Natural Risk Statisticsmentioning

confidence: 99%

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Risk measures on the space of infinite sequences

Assa

Morales

2010

Math Finan Econ

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“…In particular, one should be very cautious when using the results of separating hyperplanes. For the case of m = 1 (one scenario), Ahmed et al [4] provide alternative shorter proofs for Theorems 3.1 and 3.3 using convex duality theory after seeing the first version of this paper.…”

Section: 2mentioning

confidence: 99%

“…In particular, ES is sensitive to modeling assumptions of heaviness of tail distributions and to outliers in the data, as is shown in §5. 4.…”

mentioning

confidence: 99%

External Risk Measures and Basel Accords

Kou

Peng

Heyde³

2013

Mathematics of OR

158

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DeceasedChoosing a proper external risk measure is of great regulatory importance, as exemplified in the Basel II and Basel III Accords, which use value-at-risk with scenario analysis as the risk measures for setting capital requirements. We argue that a good external risk measure should be robust with respect to model misspecification and small changes in the data. A new class of data-based risk measures called natural risk statistics is proposed to incorporate robustness. Natural risk statistics are characterized by a new set of axioms. They include the Basel II and III risk measures and a subclass of robust risk measures as special cases; therefore, they provide a theoretical framework for understanding and, if necessary, extending the Basel Accords.

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Robust External Risk Measures

Kou

Peng

Heyde

2011

Wiley Encyclopedia of Operations Research and Management Science

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Choosing a proper risk measure is an important regulatory issue, as exemplified in governmental regulations such as Basel II accord [1] and its recent revision [2], which use Value-at-Risk (VaR) with scenario analysis as the risk measure for setting capital requirement for market risk. The main motivation of this article is to investigate whether VaR with scenario analysis are good risk measures for external regulation. By using the notion of comonotonic random variables studied in decision theory literatures such as Refs 3-8, we shall propose a new class of risk measures satisfying a new set of axioms. The new class of risk measures includes VaR with scenario analysis, in particular the current and recently revised Basel II risk measures [1,2] as special cases, and therefore provides a theoretical basis for using VaR with scenario analysis as robust risk measures for the purpose of external, regulatory risk measurement.Broadly speaking, a risk measure attempts to assign a single numerical value to a random financial loss. Obviously, it can be problematic to use one number to summarize the whole statistical distribution of the financial loss. Therefore, one shall avoid doing this if it is at all possible. However, in many cases there is no other choice.

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A note on natural risk statistics

Cited by 27 publications

References 2 publications

Risk measures on the space of infinite sequences

Risk measures on the space of infinite sequences

External Risk Measures and Basel Accords

Robust External Risk Measures

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