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摘要翻译：
我们应用Malliavin-Thalmaier-Watanabe的结果讨论了扰动随机微分方程解的强Taylor展开式和弱Taylor展开式。特别地，我们给出了展开式的泰勒系数的权重表达式。将所得结果应用于LIBOR市场模型，以处理典型的随机漂移和随机波动。与其它精确的方法如完全SDE的数值格式相比，我们得到了精确定价的易于处理的表达式。特别是，我们提出了一个易于处理的替代“冻结漂移”在LIBOR市场模型，其精度类似于完整的数值方案。数值算例说明了结果。
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英文标题：
《Weak and Strong Taylor methods for numerical solutions of stochastic
differential equations》
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作者：
Maria Siopacha and Josef Teichmann
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最新提交年份：
2007
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
We apply results of Malliavin-Thalmaier-Watanabe for strong and weak Taylor expansions of solutions of perturbed stochastic differential equations (SDEs). In particular, we work out weight expressions for the Taylor coefficients of the expansion. The results are applied to LIBOR market models in order to deal with the typical stochastic drift and with stochastic volatility. In contrast to other accurate methods like numerical schemes for the full SDE, we obtain easily tractable expressions for accurate pricing. In particular, we present an easily tractable alternative to ``freezing the drift'' in LIBOR market models, which has an accuracy similar to the full numerical scheme. Numerical examples underline the results.
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PDF链接：
https://arxiv.org/pdf/0704.0745
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