First order strong approximations of scalar SDEs defined in a domain

We are interested in strong approximations of one-dimensional SDEs which have non-Lipschitz coefficients and which take values in a domain. Under a set of general assumptions we derive an implicit scheme that preserves the domain of the SDEs and is strongly convergent with rate one. Moreover, we sho...

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Bibliographic Details
Published inNumerische Mathematik Vol. 128; no. 1; pp. 103 - 136
Main Authors Neuenkirch, Andreas, Szpruch, Lukasz
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2014
Subjects
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Simulation
Theoretical
65J15
60H10
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Summary:We are interested in strong approximations of one-dimensional SDEs which have non-Lipschitz coefficients and which take values in a domain. Under a set of general assumptions we derive an implicit scheme that preserves the domain of the SDEs and is strongly convergent with rate one. Moreover, we show that this general result can be applied to many SDEs we encounter in mathematical finance and bio-mathematics. We will demonstrate flexibility of our approach by analyzing classical examples of SDEs with sublinear coefficients (CIR, CEV models and Wright–Fisher diffusion) and also with superlinear coefficients (3/2-volatility, Aït-Sahalia model). Our goal is to justify an efficient Multilevel Monte Carlo method for a rich family of SDEs, which relies on good strong convergence properties.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-014-0606-4