Exact Simulation of reciprocal Archimedean copulas

TL;DR

This paper extends exact simulation methods from extreme-value copulas to a broader family of max-infinitely divisible distributions, including reciprocal Archimedean copulas, by leveraging properties of Poisson random measures.

Contribution

It generalizes existing simulation algorithms to reciprocal Archimedean copulas using Poisson process representations.

Findings

Provides a new exact simulation approach for reciprocal Archimedean copulas.

Extends the class of copulas that can be simulated exactly.

Connects Poisson random measures with copula simulation techniques.

Abstract

The decreasing enumeration of the points of a Poisson random measure whose mean measure has finite survival function on the positive half-axis can be represented as a non-increasing function of the jump times of a standard Poisson process. This observation allows to generalize the essential idea from a well-known exact simulation algorithm for arbitrary extreme-value copulas to copulas of a more general family of max-infinitely divisible distributions, with reciprocal Archimedean copulas being a particular example.