Open Access
May 2016 Exchangeable exogenous shock models
Jan-Frederik Mai, Steffen Schenk, Matthias Scherer
Bernoulli 22(2): 1278-1299 (May 2016). DOI: 10.3150/14-BEJ693


We characterize a comprehensive family of $d$-variate exogenous shock models. Analytically, we consider a family of multivariate distribution functions that arises from ordering, idiosyncratically distorting, and finally multiplying the arguments. Necessary and sufficient conditions on the involved distortions to yield a multivariate distribution function are given. Probabilistically, the attainable set of distribution functions corresponds to a large class of exchangeable exogenous shock models. Besides, the vector of exceedance times of an increasing additive stochastic process across independent exponential trigger variables is shown to constitute an interesting subclass of the considered distributions and yields a second probabilistic model. The alternative construction is illustrated in terms of two examples.


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Jan-Frederik Mai. Steffen Schenk. Matthias Scherer. "Exchangeable exogenous shock models." Bernoulli 22 (2) 1278 - 1299, May 2016.


Received: 1 April 2014; Revised: 1 September 2014; Published: May 2016
First available in Project Euclid: 9 November 2015

zbMATH: 06562311
MathSciNet: MR3449814
Digital Object Identifier: 10.3150/14-BEJ693

Keywords: additive process , copula , exogenous shock model , frailty-model , multivariate distribution function

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 2 • May 2016
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