Hybrid Adaptive Multilevel Monte Carlo Algorithm for Non-Smooth Observables of Itô Stochastic Differential Equations

Handle URI:
http://hdl.handle.net/10754/624002
Title:
Hybrid Adaptive Multilevel Monte Carlo Algorithm for Non-Smooth Observables of Itô Stochastic Differential Equations
Authors:
Rached, Nadhir B.; Hoel, Haakon; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
A new hybrid adaptive MC forward Euler algorithm for SDEs with singular coefficients and non-smooth observables is developed. This adaptive method is based on the derivation of a new error expansion with computable leading order terms. When a non-smooth binary payoff is considered, the new adaptive method achieves the same complexity as the uniform discretization with smooth problems. Moreover, the new developed algorithm is extended to the multilevel Monte Carlo (MLMC) forward Euler setting which reduces the complexity from O(TOL-3) to O(TOL-2(log(TOL))2). For the binary option case, it recovers the standard multilevel computational cost O(TOL-2(log(TOL))2). When considering a higher order Milstein scheme, a similar complexity result was obtained by Giles using the uniform time stepping for one dimensional SDEs, see [2]. The difficulty to extend Giles’ Milstein MLMC method to the multidimensional case is an argument for the flexibility of our new constructed adaptive MLMC forward Euler method which can be easily adapted to this setting. Similarly, the expected complexity O(TOL-2(log(TOL))2) is reached for the multidimensional case and verified numerically.
KAUST Department:
Computer, Electrical and Mathematical Sciences & Engineering (CEMSE)
Conference/Event name:
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2014)
Issue Date:
6-Jan-2014
Type:
Poster
Appears in Collections:
Posters; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2014)

Full metadata record

DC FieldValue Language
dc.contributor.authorRached, Nadhir B.en
dc.contributor.authorHoel, Haakonen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2017-06-01T10:20:43Z-
dc.date.available2017-06-01T10:20:43Z-
dc.date.issued2014-01-06-
dc.identifier.urihttp://hdl.handle.net/10754/624002-
dc.description.abstractA new hybrid adaptive MC forward Euler algorithm for SDEs with singular coefficients and non-smooth observables is developed. This adaptive method is based on the derivation of a new error expansion with computable leading order terms. When a non-smooth binary payoff is considered, the new adaptive method achieves the same complexity as the uniform discretization with smooth problems. Moreover, the new developed algorithm is extended to the multilevel Monte Carlo (MLMC) forward Euler setting which reduces the complexity from O(TOL-3) to O(TOL-2(log(TOL))2). For the binary option case, it recovers the standard multilevel computational cost O(TOL-2(log(TOL))2). When considering a higher order Milstein scheme, a similar complexity result was obtained by Giles using the uniform time stepping for one dimensional SDEs, see [2]. The difficulty to extend Giles’ Milstein MLMC method to the multidimensional case is an argument for the flexibility of our new constructed adaptive MLMC forward Euler method which can be easily adapted to this setting. Similarly, the expected complexity O(TOL-2(log(TOL))2) is reached for the multidimensional case and verified numerically.en
dc.subjectSamplingen
dc.titleHybrid Adaptive Multilevel Monte Carlo Algorithm for Non-Smooth Observables of Itô Stochastic Differential Equationsen
dc.typePosteren
dc.contributor.departmentComputer, Electrical and Mathematical Sciences & Engineering (CEMSE)en
dc.conference.dateJanuary 6-10, 2014en
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2014)en
dc.conference.locationKAUSTen
kaust.authorRached, Nadhir B.en
kaust.authorHoel, Haakonen
kaust.authorTempone, Raulen
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