Exact Simulation of the Extrema of Stable Processes

Jorge Ignacio González Cázares, Aleksandar Mijatović, Gerónimo Uribe Bravo
6/5/2018
math.PRstat.CO

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Abstract

We exhibit an exact simulation algorithm for the supremum of a stable process over a finite time interval using dominated coupling from the past (DCFTP). We establish a novel perpetuity equation for the supremum (via the representation of the concave majorants of Lévy processes) and apply it to construct a Markov chain in the DCFTP algorithm. We prove that the number of steps taken backwards in time before the coalescence is detected is finite. We analyse numerically the performance of the algorithm (the code, written in Julia 1.0, is available on GitHub).

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Cite this paper

@article{czares2018exact,
  title  = {Exact Simulation of the Extrema of Stable Processes},
  author = {Jorge Ignacio González Cázares and Aleksandar Mijatović and Gerónimo Uribe Bravo},
  year   = {2018},
  eprint = {1806.01870},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/1806.01870}
}

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