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title:
A deterministic algorithm based on discretized Wagner-Platen steps for quadrature of marginals of SDEs |
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name:
Yaroslavtseva |
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first name:
Larisa
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location/conference:
SPP-JT13
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PRESENTATION-link:
http://www.dfg-spp1324.de/nuhagtools/event_NEW/dateien/SPP-JT13/talks/Yaroslavtseva_JT13.pdf |
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abstract:
We consider the problem of approximating the expectation
Ef(X(1)) of a function f of the solution X of a d-dimensional system of stochastic differential equations (SDE) at time point 1. We present
a deterministic algorithm, which is based on a quadrature rule obtained by iteratively applying a
discretized Wagner-Platen step together with strategies to reduce the diameter and the size of the
support of a discrete measure. For Lipschitz continuous integrands f and smooth enough coefficients
of the SDE this algorithm almost achieves an error of order 1/d in terms of its computational cost.
We further present lower bounds for the error of arbitrary deterministic algorithms in worst case
settings with respect to classes of SDEs and classes of integrands defined in terms of smoothness
constraints. In particular, it turns out that our algorithm is almost asymptotically optimal.
This is joint work with Thomas Mueller-Gronbach (Passau) and Klaus Ritter (Kaiserslautern). |
