作者提出了一种新的简单算法，用于在[1]和[2]的精神下弱逼近随机微分方程。他们将该算法应用于Heston随机波动模型下的亚式期权定价问题，并与其他已知方法进行了比较。结果表明，该算法与拟蒙特卡洛方法相结合可使计算速度极快。 [1] Shigeo Kusuoka，“扩散过程期望的逼近与数理金融”，《纯数学高级研究》，1998年奈良最终谷口研讨会论文集（T. Sunada编），第31卷，2001年，第147-165页。[2] Terry Lyons和Nicolas Victoir，“Wiener空间上的求体积”，《伦敦皇家学会会刊A辑：数学与物理科学》，第460卷，2004年，第169-198页。
英文摘要：
The authors present a new simple algorithm to approximate weakly stochastic differential equations in the spirit of [1] and [2]. They apply it to the problem of pricing Asian options under the Heston stochastic volatility model, and compare it with other known methods. It is shown that the combination of the suggested algorithm and quasi-Monte Carlo methods makes computations extremely fast.
[1] Shigeo Kusuoka, ``Approximation of Expectation of Diffusion Process and Mathematical Finance,'' Advanced Studies in Pure Mathematics, Proceedings of Final Taniguchi Symposium, Nara 1998 (T. Sunada, ed.), vol. 31 2001, pp. 147--165. [2] Terry Lyons and Nicolas Victoir, ``Cubature on Wiener Space,'' Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 460 (2004), pp. 169--198.
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