An Explicit Euler Scheme with Strong Rate of Convergence for Financial SDEs with Non-Lipschitz Coefficients
An Explicit Euler Scheme with Strong Rate of Convergence for Financial SDEs with Non-Lipschitz Coefficients
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DOI：
10.1137/15m1017788
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发表时间：
2014-05
期刊：
影响因子：
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通讯作者：
J. Chassagneux;A. Jacquier;I. Mihaylov
中科院分区：
文献类型：
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作者：
J. Chassagneux;A. Jacquier;I. Mihaylov
本文研究具有非Lipschitz漂移或扩散系数的随机微分方程的逼近问题。我们提出了一个修改后的显式欧拉-丸山离散计划，使我们能够证明强收敛，与速度。在一定的正则性和可积性条件下，得到了最优强错误率。我们将这一方案应用于金融数学文献中广泛使用的随机微分方程，包括Cox-Ingersoll-Ross~（CIR）模型、3/2模型和Ait-Sahalia模型，以及一族具有局部光滑系数的均值回复过程。我们数值说明了该计划的强收敛性，并证明了其效率在多级Monte Carlo设置。
We consider the approximation of stochastic differential equations (SDEs) with non-Lipschitz drift or diffusion coefficients. We present a modified 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.