英文标题：
《Neural network regression for Bermudan option pricing》
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作者：
Bernard Lapeyre (CERMICS, MATHRISK), J\\\'er\\^ome Lelong (DAO)
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最新提交年份：
2020
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英文摘要：
  The pricing of Bermudan options amounts to solving a dynamic programming principle, in which the main difficulty, especially in high dimension, comes from the conditional expectation involved in the computation of the continuation value. These conditional expectations are classically computed by regression techniques on a finite dimensional vector space. In this work, we study neural networks approximations of conditional expectations. We prove the convergence of the well-known Longstaff and Schwartz algorithm when the standard least-square regression is replaced by a neural network approximation. We illustrate the numerical efficiency of neural networks as an alternative to standard regression methods for approximating conditional expectations on several numerical examples.
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中文摘要：
百慕大期权的定价相当于求解一个动态规划原理，其中的主要困难，尤其是在高维情况下，来自计算连续值所涉及的条件期望。这些条件期望是通过有限维向量空间上的回归技术进行经典计算的。在这项工作中，我们研究了条件期望的神经网络近似。当标准最小二乘回归被神经网络近似代替时，我们证明了著名的Longstaff和Schwartz算法的收敛性。我们通过几个数值例子说明了神经网络作为标准回归方法的替代方法在逼近条件期望方面的数值效率。
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分类信息：

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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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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