Stochastic distortion and stochastic distorted copula

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