英文标题：
《A primal-dual algorithm for BSDEs》
---
作者：
Christian Bender, Nikolaus Schweizer, Jia Zhuo
---
最新提交年份：
2014
---
英文摘要：
  We generalize the primal-dual methodology, which is popular in the pricing of early-exercise options, to a backward dynamic programming equation associated with time discretization schemes of (reflected) backward stochastic differential equations (BSDEs). Taking as an input some approximate solution of the backward dynamic program, which was pre-computed, e.g., by least-squares Monte Carlo, our methodology allows to construct a confidence interval for the unknown true solution of the time discretized (reflected) BSDE at time 0. We numerically demonstrate the practical applicability of our method in two five-dimensional nonlinear pricing problems where tight price bounds were previously unavailable.
---
中文摘要：
我们将早期行使期权定价中流行的原始-对偶方法推广到一个与（反射的）倒向随机微分方程（BSDE）的时间离散方案相关的倒向动态规划方程。以预先计算的反向动态程序的近似解（例如，通过最小二乘蒙特卡罗）作为输入，我们的方法允许为时间离散（反射）BSDE在时间0处的未知真解构造置信区间。我们用数值方法证明了我们的方法在两个五维非线性定价问题中的实用性，在这些问题中，严格的价格界限以前是不可用的。
---
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
--
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
--
一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
--

---
PDF下载：
-->