Stochastic distortion and its transformed copula

Motivated by wide applications of distortion functions and copulas in insurance and finance, this paper generalizes the notion of a deterministic distortion function to a stochastic distortion, i.e., a random process, and employs the defined stochastic distortion to construct a so-called transformed copula by stochastic distortions. One method for constructing stochastic distortions is provided with a focus on using time-changed processes. After giving some families of the transformed copulas by stochastic distortions, a particular class of transformed copulas is applied to a portfolio credit risk model, where a numeric study shows the advantage of using the transformed copulas over the conventional Gaussian copula and the double t copula in terms of the fitting accuracy and the ability of catching tail dependence.