Exchangeable exogenous shock models

TL;DR

This paper characterizes a broad class of multivariate exogenous shock models, providing conditions for their distributions and exploring their probabilistic structures, including exchangeability and exceedance times.

Contribution

It introduces a comprehensive family of multivariate shock models with explicit conditions and probabilistic interpretations, expanding understanding of their structure and applications.

Findings

Characterization of multivariate distribution functions from distortions

Identification of exchangeable exogenous shock models

Connection to exceedance times of stochastic processes

Abstract

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.