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Weak approximation of ItÔ stochastic differential equations and related adaptive algorithms
KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
2000 (English)Licentiate thesis, comprehensive summary (Other scientific)
Place, publisher, year, edition, pages
Stockholm: KTH , 2000. , 17 p.
Series
Trita-NA, ISSN 0348-2952 ; 0020
Keyword [en]
Adaptive methods, A posteriori error estimates, Stochastic differential equations, Monte Carlo methods, HJM model, Option price, Bond market
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-1154ISBN: 91-7170-644-5 (print)OAI: oai:DiVA.org:kth-1154DiVA: diva2:6941
Note
QC 20100823Available from: 2001-04-09 Created: 2001-04-09 Last updated: 2010-08-23Bibliographically approved
List of papers
1. Adaptive weak approximation of stochastic differential equations
Open this publication in new window or tab >>Adaptive weak approximation of stochastic differential equations
2001 (English)In: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312, Vol. 54, no 10, 1169-1214 p.Article in journal (Refereed) Published
Abstract [en]

Adaptive time-stepping methods based on the Monte Carlo Euler method for weak approximation of Ito stochastic differential equations are developed. The main result is new expansions of the computational error, with computable leading-order term in a posteriori form, based on stochastic flows and discrete dual backward problems. The expansions lead to efficient and accurate computation of error estimates. Adaptive algorithms for either stochastic time steps or deterministic time steps are described. Numerical examples illustrate when stochastic and deterministic adaptive time steps are superior to constant time steps and when adaptive stochastic steps are superior to adaptive deterministic steps. Stochastic time steps use Brownian bridges and require more work for a given number of time steps. Deterministic time steps may yield more time steps but require less work; for example, in the limit of vanishing error tolerance, the ratio of the computational error and its computable estimate tends to 1 with negligible additional work to determine the adaptive deterministic time steps.

Keyword
step-size control, global error
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-20900 (URN)000170618900001 ()
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved
2. Monte Carlo euler approximation if HJM term structure financial models
Open this publication in new window or tab >>Monte Carlo euler approximation if HJM term structure financial models
2001 (English)In: Stochastic Numerics 2001 at ETH, Zurich, Switzerland. February 19 - 21, 2001, 2001Conference paper, Published paper (Other academic)
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-24192 (URN)
Note
QC 20100823Available from: 2010-08-23 Created: 2010-08-23 Last updated: 2010-08-25Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf