Results on Numerics for FBSDE with Drivers of Quadratic Growth
Results on Numerics for FBSDE with Drivers of Quadratic Growth
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DOI：
10.1007/978-3-642-03479-4_9
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发表时间：
2010-04
期刊：
影响因子：
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通讯作者：
P. Imkeller;Gonccalo dos Reis;Jianing Zhang
中科院分区：
文献类型：
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作者：
P. Imkeller;Gonccalo dos Reis;Jianing Zhang
研究具有二次增长驱动的正反向随机微分方程（qgFBSDE）数值逼近问题。为了说明qgFBSDE的重要性，我们讨论了一个使用相关资产的保险相关金融衍生品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，解过程的路径正则性是有帮助的。我们提出了一种基于驱动程序截断的方法，并明确地将误差估计作为截断高度的函数。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，我们通过简单保险衍生品的价格和最优对冲的模拟来说明我们的数值逼近方法。
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.