Distortions of multivariate distribution functions and associated level curves: applications in multivariate risk theory

Elena Di Bernardino (1) , Didier Rullière (2)

1 CEDRIC - Centre d'études et de recherche en informatique et communications
2 SAF - Laboratoire de Sciences Actuarielle et Financière

In this paper, we propose a parametric model for multivariate distributions. The model is based on distortion functions, i.e. some transformations of a multivariate distribution which permit to generate new families of multivariate distribution functions. We derive some properties of considered distortions. A suitable proximity indicator between level curves is introduced in order to evaluate the quality of candidate distortion parameters. Using this proximity indicator and properties of distorted level curves, we give a speci c estimation procedure. The estimation algorithm is mainly relying on straightforward univariate optimizations, and we nally get parametric representations of both multivariate distribution functions and associated level curves. Our results are motivated by applications in multivariate risk theory. The methodology is illustrated on simulated and real examples.

Mots clés: Multivariate risk measures; Multivariate probability distortions; Level sets estimation; Iterated compositions; Hyperbolic conversion functions; Multivariate risk measures.

Domaines: Applications [stat.AP]; Economies et finances; Gestion des risques [q-fin.RM]

Elena Di Bernardino, Didier Rullière. Distortions of multivariate distribution functions and associated level curves: applications in multivariate risk theory. Insurance: Mathematics and Economics, 2013, 53, pp.190-205. ⟨10.1016/j.insmatheco.2013.05.001⟩. ⟨hal-00750873v4⟩