Explicit Diversification Benefit for Dependent Risks

Dacorogna, Michel M.; Elbahtouri, Laila; Kratz, Marie

doi:10.2139/ssrn.2716093

Cited by 8 publications

(10 citation statements)

References 6 publications

(18 reference statements)

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“…Deploying on different methodologies, this formula was obtained by Guillén et al (2013), Dacarogna et al (2015) and Sarabia et al (2016). As the pdf (15) is a second kind beta distribution S n ∼ B2(α, n, β) (see McDonald, 1984).…”

Section: Proofmentioning

confidence: 99%

Aggregation of Dependent Risks in Mixtures of Exponential Distributions and Extensions

Sarabia

Gómez–Déniz²,

Prieto³

et al. 2018

ASTIN Bull.

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The distribution of the sum of dependent risks is a crucial aspect in actuarial sciences, risk management and in many branches of applied probability. In this paper, we obtain analytic expressions for the probability density function (pdf) and the cumulative distribution function (cdf) of aggregated risks, modeled according to a mixture of exponential distributions. We first review the properties of the multivariate mixture of exponential distributions, to then obtain the analytical formulation for the pdf and the cdf for the aggregated distribution. We study in detail some specific families with Pareto (Sarabia et al, 2016), Gamma, Weibull and inverse Gaussian mixture of exponentials (Whitmore and Lee, 1991) claims. We also discuss briefly the computation of risk measures, formulas for the ruin probability (Albrecher et al., 2011) and the collective risk model. An extension of the basic model based on mixtures of gamma distributions is proposed, which is one of the suggested directions for future research. .es (V. Jordá). The modelLet Θ be a positive random variable with cdf F Θ (·) and Laplace-Stieltjes transform (hereinafter referred to as Laplace transform) L Θ (·), that is L Θ (s) = E[exp(−sΘ)] = ∞ 0 e −sz dF Θ (z). A distribution with support on (0, ∞) is identified by its Laplace transform. We consider the classical compound

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Section: Proofmentioning

confidence: 99%

Aggregation of Dependent Risks in Mixtures of Exponential Distributions and Extensions

Sarabia

Gómez–Déniz²,

Prieto³

et al. 2018

ASTIN Bull.

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“…It is the path explored in [6] where we give explicit formulae for the aggregation of Pareto distributions coupled via a Clayton survival copulae and Weibull distributions coupled with Gumbel copulae. In Figure 3, we present results for the normalized TVaR (Expected Shortfall) (T V aR/n) for various tail indices α = 1.1, 23 and different level of aggregation n = 2, 10, 100.…”

Section: Testing the Convergence Of Monte Carlo Simulationsmentioning

confidence: 99%

Approaches and Techniques to Validate Internal Model Results

Dacorogna¹

2017

SSRN Journal

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The development of risk model for managing portfolio of financial institutions and insurance companies require both from the regulatory and management points of view a strong validation of the quality of the results provided by internal risk models. In Solvency II for instance, regulators ask for independent validation reports from companies who apply for the approval of their internal models.Unfortunately, the usual statistical techniques do not work for the validation of risk models as we lack enough data to significantly test the results of the models. We will certainly never have enough data to statistically estimate the significance of the VaR at a probability of 1 over 200 years, which is the risk measure required by Solvency II. Instead, we need to develop various strategies to test the reasonableness of the model.In this paper, we review various ways, management and regulators can gain confidence in the quality of models. It all starts by ensuring a good calibration of the risk models and the dependencies between the various risk drivers. Then applying stress tests to the model and various empirical analysis, in particular the probability integral transform, we build a full and credible framework to validate risk models.

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“…The diversification index associated with VaR under different assumptions on the marginal distributions and dependence structure, as well as its asymptotic limits can be found in the literature (see e.g. Bürgi et al (2008), Dacorogna et al (2015), Degen et al (2010), Embrechts et al (1997). We denote the diversification index D VaR β as D β to emphasize the role of β in the calculation of the index.…”

Section: Risk Measures and Diversificationmentioning

confidence: 99%

Diversification Benefits Under Multivariate Second Order Regular Variation

Das

Kratz

2017

SSRN Journal

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We analyze risk diversification in a portfolio of heavy-tailed risk factors under the assumption of second order multivariate regular variation. Asymptotic limits for a measure of diversification benefit are obtained when considering, for instance, the value-at-risk . The asymptotic limits are computed in a few examples exhibiting a variety of different assumptions made on marginal or joint distributions. This study ties up existing related results available in the literature under a broader umbrella.

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Explicit Diversification Benefit for Dependent Risks

Cited by 8 publications

References 6 publications

Aggregation of Dependent Risks in Mixtures of Exponential Distributions and Extensions

Aggregation of Dependent Risks in Mixtures of Exponential Distributions and Extensions

Approaches and Techniques to Validate Internal Model Results

Diversification Benefits Under Multivariate Second Order Regular Variation

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