Marshall–Olkin Machinery and Power Mixing: The Mixed Generalized Marshall–Olkin Distribution

Mulinacci, Sabrina

doi:10.1007/978-3-319-19039-6_5

Cited by 6 publications

(4 citation statements)

References 19 publications

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“…In this section we briefly review the case of unobservable shocks linked by an Archimedean copula. The model presented is a particular case of that studied in Mulinacci (2015) and Mulinacci (2018) where the possibility of more than one shock affecting different subsets of the considered lifetimes is allowed. We summarize here the model, restricted to one common shock, for the sake of completeness and easyness of the reader.…”

Section: The Exchangeable Dependence Case Modelmentioning

confidence: 99%

“…The first contribution in this direction was due to Li (2009), in which the dependence induced by a mixing procedure is considered. More general frameworks in which both the assumption of independence as well as that of marginal distributions of exponential type are relaxed, are considered, among the others, in Durante et al (2010), Bernhart et al (2013), and Mulinacci (2015Mulinacci ( , 2018.…”

Section: Introductionmentioning

confidence: 99%

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Hierarchical Archimedean Dependence in Common Shock Models

Cherubini

Mulinacci

2020

Methodol Comput Appl Probab

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In this paper we show how to extend a simple common shock model with Archimedean dependence of the hidden variables to the non-exchangeable case. The assumption is that the hidden risk factors are linked by a hierarchical Archimedean dependence structure, possibly fully nested . We give directions about how to implement the model and to address the issue that the hidden variables must be put in descending dependence order. We show how the model can be simplified in the Gumbel-Marshall-Olkin distribution in Cherubini and Mulinacci (2017), the only case in which exponential distribution of the observed variables is preserved.

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Section: The Exchangeable Dependence Case Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hierarchical Archimedean Dependence in Common Shock Models

Cherubini

Mulinacci

2020

Methodol Comput Appl Probab

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“…Such distributions and prominent subfamilies, like max-(or min-) stable laws, are well-established in the applied probability and statistics literature, see e.g. [3,46,2,28,49,16], and have recently gained interest in the modeling of spatial extremes, see [22,8,50,23]. In analytical terms, such probability distributions are canonically described by a so-called exponent measure and the work of [59,17] generalizes this framework to infinite sequences of random variables.…”

Section: Introductionmentioning

confidence: 99%

Exchangeable min-id sequences: Characterization, exponent measures and non-decreasing id-processes

Brück¹,

Mai²,

Scherer³

2020

Preprint

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We establish a correspondence between exchangeable sequences of random variables whose finite-dimensional distributions are min-(or max-) infinitely divisible and non-negative, non-decreasing, infinitely divisible stochastic processes. The exponent measure of a min-id sequence is shown to be the sum of a very simple "drift measure" and a mixture of product probability measures, which corresponds uniquely to the Lévy measure of a non-decreasing infinitely divisible process. The latter is shown to be supported on non-negative and non-decreasing functions. Our results provide an analytic umbrella which embeds the de Finetti subfamilies of many classes of multivariate distributions, such as exogenous shock models, exponential and geometric laws with lack-of-memory property, minstable multivariate exponential and extreme-value distributions, as well as reciprocal Archimedean copulas with completely monotone generator and Archimedean copulas with log-completely monotone generator.

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“…On the other side, the approach of allowing for general marginal distributions in place of the exponential one, even preserving the independence, is studied in Li and Pellerey (2011) in the bivariate case and extended to the multidimensional case in Lin and Li (2014): they call their distribution generalized Marshall-Olkin distribution. Scale-mixtures of the generalized Marshall-Olkin distribution are considered in Mulinacci (2015), with the aim, again, to introduce a specific Archimedean dependence (the generator is again given by the Laplace tranform of the mixing variable) among the underlying shocks arrival times: the case of an underlying Archimedean dependence with a fully general generator is analyzed in Mulinacci (2017). The union of Marshall-Olkin and Archimedean dependence structures is also studied in Charpentier et al (2014).…”

Section: Introductionmentioning

confidence: 99%

A systemic shock model for too big to fail financial institutions

Mulinacci

2017

Preprint

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In this paper we study the distributional properties of a vector of lifetimes in which each lifetime is modeled as the first arrival time between an idiosyncratic shock and a common systemic shock. Despite unlike the classical multidimensional Marshall-Olkin model here only a unique common shock affecting all the lifetimes is assumed, some dependence is allowed between each idiosyncratic shock arrival time and the systemic shock arrival time. The dependence structure of the resulting distribution is studied through the analysis of its singularity and its associated copula function. Finally, the model is applied to the analysis of the systemic riskiness of those European banks classified as systemically important (SIFI).

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Marshall–Olkin Machinery and Power Mixing: The Mixed Generalized Marshall–Olkin Distribution

Cited by 6 publications

References 19 publications

Hierarchical Archimedean Dependence in Common Shock Models

Hierarchical Archimedean Dependence in Common Shock Models

Exchangeable min-id sequences: Characterization, exponent measures and non-decreasing id-processes

A systemic shock model for too big to fail financial institutions

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