dc.contributor.author Rached, Nadhir B. dc.contributor.author Hoel, Hakon dc.contributor.author Tempone, Raul dc.date.accessioned 2017-06-01T10:20:43Z dc.date.available 2017-06-01T10:20:43Z dc.date.issued 2014-01-06 dc.identifier.uri http://hdl.handle.net/10754/624002 dc.description.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. dc.subject Sampling dc.title Hybrid Adaptive Multilevel Monte Carlo Algorithm for Non-Smooth Observables of Itô Stochastic Differential Equations dc.type Poster dc.contributor.department Applied Mathematics and Computational Science Program dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.conference.date January 6-10, 2014 dc.conference.name Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2014) dc.conference.location KAUST kaust.person Rached, Nadhir B. kaust.person Hoel, Hakon kaust.person Tempone, Raul refterms.dateFOA 2018-06-14T04:27:24Z
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