Mathematics in Finance
Mathematics in Finance
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金融数学
DOI：
10.1090/conm/515/10120
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Gyurkó L
中科院分区：
文献类型：
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作者：
Gyurkó L
本文将[3]和[7]的渐近估计与粗糙路径观点（[13]，[14]）相结合，给出了一个推导随机微分方程高阶、稳定和易处理的路径逼近的一般框架。该方法可以追溯到[17]，可能更早，基于局部推导和求解随机常微分方程。当局部阶为g时，给出了保证全局阶为g1/2的数值常微分方程解精度的一个充分条件.我们还指出了一些实用的解决方案，使高阶格式易于处理。
The paper connects asymptotic estimations of [3] and [7] with the Rough Paths perspective ([13], [14]) to present a general framework for deriving high order, stable and tractable path-wise approximations of stochastic differential equations. The approach, which can be traced back to [17] and probably earlier, is based on locally deriving and solving random ordinary differential equations. A sufficient condition on the accuracy of the numerical ODE solver is given to ensure the global order is g1/2 if the local order is g. We also point out some practical solutions which make the high order schemes tractable.