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摘要翻译：
研究了具有二次增长驱动的正倒向随机微分方程的数值逼近问题。为了说明qgFBSDE的意义，我们讨论了一个使用相关资产的保险相关金融衍生工具的交叉套期保值问题。对于这类随机方程组的数值逼近格式的收敛性，求解过程的路径正则性是重要的。我们提出了一种基于驱动器截断的方法，并将误差估计显式地表示为截断高度的函数。利用Cole-Hopf指数变换，讨论了具有全局Lipschitz连续驱动的FBSDE的约简方法。最后，通过对简单保险衍生品的价格和最优套期保值的模拟，说明了我们的数值逼近方法。
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英文标题：
《Results on numerics for FBSDE with drivers of quadratic growth》
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作者：
Peter Imkeller and Gon\c{c}alo dos Reis and Jianing Zhang
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最新提交年份：
2010
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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 consider the problem of numerical approximation for forward-backward stochastic differential equations with drivers of quadratic growth (qgFBSDE). To illustrate the significance of qgFBSDE, we discuss a problem of cross hedging of an insurance related financial derivative using correlated assets. For the convergence of numerical approximation schemes for such systems of stochastic equations, path regularity of the solution processes is instrumental. We present a method based on the truncation of the driver, and explicitly exhibit error estimates as functions of the truncation height. We discuss a reduction method to FBSDE with globally Lipschitz continuous drivers, by using the Cole-Hopf exponential transformation. We finally illustrate our numerical approximation methods by giving simulations for prices and optimal hedges of simple insurance derivatives.
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PDF链接：
https://arxiv.org/pdf/1004.2248
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