Exact simulation of continuous max-id processes

An algorithm for the unbiased simulation of max-(or min-)id stochastic processes is developed. Our algorithm only requires the simulation of finite Poisson random measures and avoids the necessity of computing conditional distributions of infinite (exponent)measures. Special emphasis is put on the simulation of exchangeable max-(or min-)id sequences, in particular exchangeable Sato-frailty sequences. Additionally, exact simulation schemes of high-dimensional exchangeable exogenous shock models and exchangeable max-stable sequences are sketched.