eprintid: 1325568 rev_number: 44 eprint_status: archive userid: 608 dir: disk0/01/32/55/68 datestamp: 2011-10-12 05:40:52 lastmod: 2021-10-04 01:18:43 status_changed: 2018-07-04 13:25:07 type: article metadata_visibility: show item_issues_count: 0 creators_name: Beskos, A creators_name: Peluchetti, S creators_name: Roberts, G title: epsilon-Strong simulation of the Brownian path ispublished: pub divisions: UCL divisions: B04 divisions: C06 divisions: F61 keywords: Brownian bridge, intersection layer, iterative algorithm, option pricing, pathwise convergence, unbiased sampling note: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. abstract: We present an iterative sampling method which delivers upper and lower bounding processes for the Brownian path. We develop such processes with particular emphasis on being able to unbiasedly simulate them on a personal computer. The dominating processes converge almost surely in the supremum and L1L1 norms. In particular, the rate of converge in L1L1 is of the order O(K−1/2)O(K−1/2), KK denoting the computing cost. The a.s. enfolding of the Brownian path can be exploited in Monte Carlo applications involving Brownian paths whence our algorithm (termed the εε-strong algorithm) can deliver unbiased Monte Carlo estimators over path expectations, overcoming discretisation errors characterising standard approaches. We will show analytical results from applications of the εε-strong algorithm for estimating expectations arising in option pricing. We will also illustrate that individual steps of the algorithm can be of separate interest, giving new simulation methods for interesting Brownian distributions. date: 2012-11 publisher: INT STATISTICAL INST official_url: https://doi.org/10.3150/11-BEJ383 vfaculties: VMPS oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_source: WoS-Lite elements_id: 344322 doi: 10.3150/11-BEJ383 lyricists_name: Beskos, Alexandros lyricists_id: ABESK05 full_text_status: public publication: Bernoulli volume: 18 number: 4 pagerange: 1223-1248 pages: 26 issn: 1350-7265 citation: Beskos, A; Peluchetti, S; Roberts, G; (2012) epsilon-Strong simulation of the Brownian path. Bernoulli , 18 (4) pp. 1223-1248. 10.3150/11-BEJ383 <https://doi.org/10.3150/11-BEJ383>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/1325568/1/beskos_stefano.pdf