An explicit Euler scheme with strong rate of convergence for non-Lipschitz SDEs

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Title: An explicit Euler scheme with strong rate of convergence for non-Lipschitz SDEs
Author(s): Chassagneux, JFC
Jacquier, A
Mihyalov, IM
Item Type: Journal Article
Abstract: We consider the approximation of one-dimensional stochastic differential equations (SDEs) with non-Lipschitz drift or diffusion coefficients. We present a modi- fied explicit Euler-Maruyama discretisation scheme that allows us to prove strong convergence, with a rate. Under some regularity and integrability conditions, we obtain the optimal strong error rate. We apply this scheme to SDEs widely used in the mathematical finance literature, including the Cox-Ingersoll-Ross (CIR), the 3/2 and the Ait-Sahalia models, as well as a family of mean-reverting processes with locally smooth coefficients. We numerically illustrate the strong convergence of the scheme and demonstrate its efficiency in a multilevel Monte Carlo setting.
Date of Acceptance: 29-Aug-2016
ISSN: 1945-497X
Publisher: Society for Industrial and Applied Mathematics
Journal / Book Title: SIAM Journal on Financial Mathematics
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/M008436/1
Copyright Statement: This article is under embargo until publication
Keywords: 0102 Applied Mathematics
Publication Status: Accepted
Embargo Date: publication subject to indefinite embargo
Appears in Collections:Financial Mathematics
Faculty of Natural Sciences

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