Exact simulation of continuous max-id processes with applications to exchangeable max-id sequences

Abstract

An algorithm for the unbiased simulation of continuous max-(resp. min-) infinitely divisible stochastic processes is developed. The algorithm only requires the simulation of finite Poisson random measures on the space of continuous functions and avoids the necessity of computing conditional distributions of infinite (exponent) measures. The complexity of the algorithm is characterized in terms of the expected number of simulated atoms of the Poisson random measures on the space of continuous functions. Special emphasis is put on the simulation of exchangeable max-(or min-) infinitely divisible sequences, in particular exchangeable Sato-frailty sequences. Additionally, exact simulation schemes of exchangeable exogenous shock models and exchangeable max-stable sequences are sketched.