An axiomatic characterization of capital allocations of coherent risk measures

Kalkbrener, Michael

doi:10.1080/14697680902814266

Cited by 11 publications

(10 citation statements)

References 23 publications

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“…We define also some desirable properties that an optimal allocation must naturally satisfy. These properties are based on the ideas presented by Artzner et al (1999) [1] for coherent risk measures and on the axiomatic characterization of coherent capital allocations given by Kalkbrener (2009) [17].…”

Section: Other Desirable Propertiesmentioning

confidence: 99%

On a capital allocation by minimization of some risk indicators

2016

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International audienceEuropean insurance sector will soon be faced with the application of the Solvency 2 regulation norms. It will create a real change in the risk management of insurance practices. The ORSA (Own Risk and Solvency Assessment) approach of the second pillar makes the capital allocation an important exercise for all insurers, especially when it comes to groups. Considering multi-branches firms, a capital allocation has to be based on multivariate risk modeling. Several allocation methods are present in the actuarial literature and insurance practices. In this paper, we focus on a risk allocation method. By minimizing some of the multivariate risk indicators, we study the coherence of the risk allocation using an axiomatic approach. Furthermore, we discuss what can be the best allocation choice for an insurance group

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Section: Other Desirable Propertiesmentioning

confidence: 99%

On a capital allocation by minimization of some risk indicators

2016

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“…Kalkbrener [13,14] suggested another axiomatic approach to capital allocation with univariate risk measures, under a basic assumption that the risk capital allocated to X i only depends on X i and X, but not on the decomposition of the rest…”

Section: Introductionmentioning

confidence: 99%

“…The main contribution of this paper is the multivariate extension of the axiomatic approach in Kalkbrener [13,14] by incorporating both the model-free models and model-dependent models into a unified setup. Meanwhile, an example (i.e.…”

Section: Introductionmentioning

confidence: 99%

Capital Allocation With Multivariate Risk Measures: An Axiomatic Approach

Wei

2019

Prob. Eng. Inf. Sci.

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Capital allocation is of central importance in portfolio management and risk-based performance measurement. Capital allocations for univariate risk measures have been extensively studied in the finance literature. In contrast to this situation, few papers dealt with capital allocations for multivariate risk measures. In this paper, we propose an axiom system for capital allocation with multivariate risk measures. We first recall the class of the positively homogeneous and subadditive multivariate risk measures, and provide the corresponding representation results. Then it is shown that for a given positively homogeneous and subadditive multivariate risk measure, there exists a capital allocation principle. Furthermore, the uniqueness of the capital allocation principe is characterized. Finally, examples are also given to derive the explicit capital allocation principles for the multivariate risk measures based on mean and standard deviation, including the multivariate mean-standard-deviation risk measures.

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“…The second condition is called the linear diversification property of capital allocation. In fact, this condition has a one to one correspondence with the positive homogeneity and subadditivity of a coherent risk measure ρ (see [25]). Since we work in this paper with a coherent risk measure it is somehow natural to adopt this definition of capital allocation.…”

Section: Definitionmentioning

confidence: 99%

“…The authors in [24] study the capital allocation problem by introducing the class of weighted risk capital allocations. A different approach to the problem of capital allocation were introduced in [25] where the author introduces an axiomatic allocation framework to study the problem. In [26] the author studies the optimal capital allocation in a way to minimize the asymptotic ruin probability.…”

Section: Literature Reviewmentioning

confidence: 99%

On the Capital Allocation Problem for a New Coherent Risk Measure in Collective Risk Theory

Assa

Morales

Firouzi

2016

Risks

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Abstract:In this paper we introduce a new coherent cumulative risk measure on a subclass in the space of càdlàg processes. This new coherent risk measure turns out to be tractable enough within a class of models where the aggregate claims is driven by a spectrally positive Lévy process. We focus our motivation and discussion on the problem of capital allocation. Indeed, this risk measure is well-suited to address the problem of capital allocation in an insurance context. We show that the capital allocation problem for this risk measure has a unique solution determined by the Euler allocation method. Some examples and connections with existing results as well as practical implications are also discussed.

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An axiomatic characterization of capital allocations of coherent risk measures

Cited by 11 publications

References 23 publications

On a capital allocation by minimization of some risk indicators

On a capital allocation by minimization of some risk indicators

Capital Allocation With Multivariate Risk Measures: An Axiomatic Approach

On the Capital Allocation Problem for a New Coherent Risk Measure in Collective Risk Theory

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