On a capital allocation by minimization of some risk indicators

Maume-Deschamps, Véronique; Rullière, Didier; Said, Khalil

doi:10.1007/s13385-016-0123-1

Cited by 8 publications

(5 citation statements)

References 22 publications

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“…We can define additional measures of systemic risk based on various capital allocation methods found in the actuarial literature. For example, we mention the optimal allocation method presented by Dhaene et al ( 2012) [14] and studied by Maume-Deschamps et al ( 2016) [26]. In this case, the systemic risk (SR) index is obtained as follows:…”

Section: Incremental Indicatormentioning

confidence: 99%

Some systemic risk indicators

El Qalli,

Said

2023

RDA

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This paper aims to introduce novel systemic risk indicators based on risk allocation methods employed in actuarial science. We present diverse general approaches for constructing these indicators and utilize them to derive indicators based on commonly used risk measures such as Value at Risk, Tail Value at Risk, and Expectiles. Furthermore, we analyze the influence of the dependence structure on the behavior of these indicators using a range of copula models. To support our findings, we provide numerical illustrations.

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Section: Incremental Indicatormentioning

confidence: 99%

Some systemic risk indicators

El Qalli,

Said

2023

RDA

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“…We now investigate properties of MLA as a risk allocation principle. For desirable properties of risk allocation in the case when the capital K is exogenously given as a constant, see Maume-Deschamps et al (2016). By construction, K M [X; K] always satisfies the full allocation property (1).…”

Section: Properties Of Mlamentioning

confidence: 99%

Modality for Scenario Analysis and Maximum Likelihood Allocation

Koike

Hofert

2020

Preprint

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We analyze dependence, tail behavior and multimodality of the conditional distribution of a loss random vector given that the aggregate loss equals an exogenously provided capital. This conditional distribution is a building block for calculating risk allocations such as the Euler capital allocation of Value-at-Risk. A level set of this conditional distribution can be interpreted as a set of severe and plausible stress scenarios the given capital is supposed to cover. We show that various distributional properties of this conditional distribution are inherited from those of the underlying joint loss distribution. Among these properties, we find that multimodality of the conditional distribution is an important feature related to the number of risky scenarios likely to occur in a stressed situation. Moreover, Euler allocation becomes less sound under multimodality than under unimodality. To overcome this issue, we propose a novel risk allocation called the maximum likelihood allocation (MLA), defined as the mode of the conditional distribution given the total capital. The process of estimating MLA turns out to be beneficial for detecting multimodality, evaluating the soundness of risk allocations, and constructing more flexible risk allocations based on multiple risky scenarios. Properties of the conditional distribution and MLA are demonstrated in numerical experiments. In particular, we observe that negative dependence among losses typically leads to multimodality, and thus to multiple risky scenarios and less sound risk allocations.

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“…For example, the variance is considered as -elicitable since Var(X) = In the context of capital allocation, the allocation may be considered as a vector-valued risk measure with k = d. In [28], an axiomatic characterization of multivariate coherence of capital allocation methods is given. It deals with, in particular, the allocation by minimizing multivariate risk indicators, which can be seen as scoring functions.…”

Section: Multivariate Elicitabilitymentioning

confidence: 99%