英文标题：
《Fast Convergence of Regress-Later Estimates in Least Squares Monte Carlo》
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作者：
Eric Beutner, Janina Schweizer, Antoon Pelsser
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最新提交年份：
2014
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英文摘要：
  Many problems in financial engineering involve the estimation of unknown conditional expectations across a time interval. Often Least Squares Monte Carlo techniques are used for the estimation. One method that can be combined with Least Squares Monte Carlo is the \"Regress-Later\" method. Unlike conventional methods where the value function is regressed on a set of basis functions valued at the beginning of the interval, the \"Regress-Later\" method regresses the value function on a set of basis functions valued at the end of the interval. The conditional expectation across the interval is then computed exactly for each basis function. We provide sufficient conditions under which we derive the convergence rate of Regress-Later estimators. Importantly, our results hold on non-compact sets. We show that the Regress-Later method is capable of converging significantly faster than conventional methods and provide an explicit example. Achieving faster convergence speed provides a strong motivation for using Regress-Later methods in estimating conditional expectations across time.
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中文摘要：
金融工程中的许多问题都涉及在一段时间间隔内对未知条件预期的估计。通常使用最小二乘蒙特卡罗技术进行估计。一种可以与最小二乘蒙特卡罗法相结合的方法是“稍后回归”法。与传统方法不同，传统方法是在区间开始时对一组基函数进行回归，而“后回归”方法是在区间结束时对一组基函数进行回归。然后为每个基函数精确计算整个区间的条件期望。我们给出了充分条件，在此条件下我们得到了回归后估计的收敛速度。重要的是，我们的结果适用于非紧集。我们证明了回归后的方法能够比传统方法更快地收敛，并提供了一个明确的例子。实现更快的收敛速度为使用后回归方法估计跨时间的条件期望提供了强大的动力。
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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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