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Fast exact simulation of the first-passage event of a subordinator

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Listed:
  • González Cázares, Jorge Ignacio
  • Lin, Feng
  • Mijatović, Aleksandar

Abstract

This paper provides an exact simulation algorithm for the sampling from the joint law of the first-passage time, the undershoot and the overshoot of a subordinator crossing a non-increasing boundary. The algorithm applies to a large non-parametric class of subordinators of interest in applications. We prove that the running time of this algorithm has finite moments of all positive orders and give an explicit bound on the expected running time in terms of the Lévy measure of the subordinator. This bound provides performance guarantees that make our algorithm suitable for Monte Carlo estimation.

Suggested Citation

  • González Cázares, Jorge Ignacio & Lin, Feng & Mijatović, Aleksandar, 2025. "Fast exact simulation of the first-passage event of a subordinator," Stochastic Processes and their Applications, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:spapps:v:183:y:2025:i:c:s0304414925000407
    DOI: 10.1016/j.spa.2025.104599
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    References listed on IDEAS

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    1. Chi, Zhiyi, 2016. "On exact sampling of the first passage event of a Lévy process with infinite Lévy measure and bounded variation," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1124-1144.
    2. Hernández-Hernández, M.E. & Kolokoltsov, V.N. & Toniazzi, L., 2017. "Generalised fractional evolution equations of Caputo type," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 184-196.
    3. Kyoung-Kuk Kim & Sojung Kim, 2016. "Simulation of Tempered Stable Lévy Bridges and Its Applications," Operations Research, INFORMS, vol. 64(2), pages 495-509, April.
    4. Devroye, Luc, 2012. "A note on generating random variables with log-concave densities," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 1035-1039.
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