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