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- W2225979086 abstract "In this article we summarise the progress made in the project Constructive Quantization and Multilevel Algorithms for Quadrature of Stochastic Differential Equations. Research was conducted along the following three lines. First we focus on deterministic quadrature formulas to approximate expectations with respect to marginal distributions of SDEs. Here we provide a complexity analysis for deterministic algorithms in a worst case setting with respect to classes of SDEs that are defined in terms of smoothness constraints on the coefficients, and we present an algorithm that is based on weak Itô-Talyor steps and performs almost asymptotically optimal. Next, we are concerned with computing expectations of quantities that depend discontinuously on the SDE at the terminal time. We present an efficient method for quadrature in the Heston model Heston model based on multilevel schemes Multilevel Monte Carlo and a Malliavin calculus-based Malliavin calculus payoff smoothing. Finally, we consider expected values of quantities that depend on the whole trajectory of a Lévy-driven SDE. We establish error estimates and central limit theorems for a multilevel Monte Carlo algorithm that achieves error rates of order $$N^{-frac{1} {2} +o(1)}$$ as the runtime N of the algorithm tends to infinity." @default.
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- W2225979086 date "2014-01-01" @default.
- W2225979086 modified "2023-10-16" @default.
- W2225979086 title "Constructive Quantization and Multilevel Algorithms for Quadrature of Stochastic Differential Equations" @default.
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- W2225979086 doi "https://doi.org/10.1007/978-3-319-08159-5_6" @default.
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