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

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    Type
    Poster
    Authors
    Rached, Nadhir B.
    Hoel, Hakon
    Tempone, Raul cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2014-01-06
    Permanent link to this record
    http://hdl.handle.net/10754/624002
    
    Metadata
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    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.
    Conference/Event name
    Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2014)
    Collections
    Posters; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2014)

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