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ε-Strong simulation of the Brownian path
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Beskos, Alexandros, Peluchetti, Stefano and Roberts, Gareth O. (2012) ε-Strong simulation of the Brownian path. Bernoulli, Volume 18 (Number 4). pp. 1223-1248. doi:10.3150/11-BEJ383 ISSN 1350-7265.
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Official URL: http://dx.doi.org/10.3150/11-BEJ383
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 L 1 norms. In particular, the rate of converge in L 1 is of the order O(K −1/2 ) , K 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 ε -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 ε -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.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Bernoulli | ||||
Publisher: | Int Statistical Institute | ||||
ISSN: | 1350-7265 | ||||
Official Date: | 12 November 2012 | ||||
Dates: |
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Volume: | Volume 18 | ||||
Number: | Number 4 | ||||
Page Range: | pp. 1223-1248 | ||||
DOI: | 10.3150/11-BEJ383 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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