Explicit ruin formulas for models with dependence among risks

Albrecher, Hansjörg; Constantinescu, Corina; Loisel, Stéphane

doi:10.1016/j.insmatheco.2010.11.007

Cited by 85 publications

(78 citation statements)

References 8 publications

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“…From the point of view of modeling extremes, more complex structures of dependence-other than exact independence-are certainly of interest, as well as tails which are heavier than the Gumbel. As discussed by Albrecher et al (2011) simple and manageable models-such as the Cramér-Lundberg modelare based on restrictive independence assumptions, but still can be used as a natural starting point for modeling.…”

Section: Discussionmentioning

confidence: 99%

On the distribution of linear combinations of independent Gumbel random variables

2014

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The distribution of linear combinations of independent Gumbel random variables is of great interest for modeling risk and extremes in the most different areas of application. In this paper we develop near-exact approximations for the distribution of linear combination of independent Gumbel random variables based on a shifted Generalized NearInteger Gamma distribution and on the distribution of the difference of two independent Generalized Integer Gamma distributions. These near-exact distributions are computationally appealing and numerical studies confirm their accuracy, as assessed by a proximity measure used in related studies. We illustrate the proposed approximations on applied problems in networks engineering, computational biology, and flood risk management.

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Section: Discussionmentioning

confidence: 99%

On the distribution of linear combinations of independent Gumbel random variables

2014

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“…Namely, practitioners often opt for those multivariate distributions that: (i) admit meaningful and relevant interpretations; (ii) allow for an adequate fit to the modelled data, be it in the 'tail', in the 'body', and/or in the dependence; and (iii) can be readily implemented. We feel that the multivariate distribution with the univariate margins distributed gamma that we put forward next (also, Albrecher et al 2011;Sarabia et al 2018) is exactly such.…”

Section: Definition and Basic Propertiesmentioning

confidence: 93%

On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance

Semenikhine

Furman

2018

Risks

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Abstract:One way to formulate a multivariate probability distribution with dependent univariate margins distributed gamma is by using the closure under convolutions property. This direction yields an additive background risk model, and it has been very well-studied. An alternative way to accomplish the same task is via an application of the Bernstein-Widder theorem with respect to a shifted inverse Beta probability density function. This way, which leads to an arguably equally popular multiplicative background risk model (MBRM), has been by far less investigated. In this paper, we reintroduce the multiplicative multivariate gamma (MMG) distribution in the most general form, and we explore its various properties thoroughly. Specifically, we study the links to the MBRM, employ the machinery of divided differences to derive the distribution of the aggregate risk random variable explicitly, look into the corresponding copula function and the measures of nonlinear correlation associated with it, and, last but not least, determine the measures of maximal tail dependence. Our main message is that the MMG distribution is (1) very intuitive and easy to communicate, (2) remarkably tractable, and (3) possesses rich dependence and tail dependence characteristics. Hence, the MMG distribution should be given serious considerations when modelling dependent risks.

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“…It has been shown by Albrecher et al (2011) (see Example 2.3 therein) that this dependence structure is equivalent to a rotated Clayton copula with parameter α, with Pareto(α, β) marginals, where the density of the rotated Clayton copula is defined as…”

Section: Illustrations On Dependence Between Capital Gains Inter-arrmentioning

confidence: 99%

On finite-time ruin probabilities in a generalized dual risk model with dependence

Dimitrova

Kaishev

Zhao

2015

European Journal of Operational Research

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Citation: Dimitrova, D. S., Kaishev, V. K. and Zhao, S. (2015). On finite-time ruin probabilities in a generalized dual risk model with dependence. European Journal of Operational Research, 242(1), pp. 134-148. doi: 10.1016Research, 242(1), pp. 134-148. doi: 10. /j.ejor.2014 This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent AbstractIn this paper, we study the finite-time ruin probability in a reasonably generalized dual risk model, where we assume any non-negative non-decreasing cumulative operational cost function and arbitrary capital gains arrival process. Establishing an enlightening link between this dual risk model and its corresponding insurance risk model, explicit expressions for the finite-time survival probability in the dual risk model are obtained under various general assumptions for the distribution of the capital gains. In order to make the model more realistic and general, different dependence structures among capital gains and inter-arrival times and between both are also introduced and corresponding ruin probability expressions are also given. The concept of alarm time, as introduced in Das and Kratz (2012), is applied to the dual risk model within the context of risk capital allocation. Extensive numerical illustrations are provided.

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Explicit ruin formulas for models with dependence among risks

Cited by 85 publications

References 8 publications

On the distribution of linear combinations of independent Gumbel random variables

On the distribution of linear combinations of independent Gumbel random variables

On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance

On finite-time ruin probabilities in a generalized dual risk model with dependence

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