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相关实验视频

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深度BSVIEs参数化和基于学习的应用程序.

Nacira Agram1, Giulia Pucci1

  • 1Department of Mathematics, KTH Royal Institute of Technology, Stockholm, 100 44, Sweden.

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|February 18, 2026
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概括
此摘要是机器生成的。

本研究介绍了一种新的数字方法,用于逆位随机伏尔特拉积分方程 (BSVIEs),这对于记忆金融建模至关重要. 深度学习方法准确地近似这些复杂方程及其反映变量的解决方案.

关键词:
这是BSVIEs的原因.深度学习是一种深度学习.神经网络的解决方案在RBSVIEs中使用.在Stricker-Yor中,可测量性是可测量的.

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科学领域:

  • 数字分析 数字分析
  • 随机过程是指随机的过程.
  • 在金融领域的机器学习.

背景情况:

  • 倒向随机伏尔特拉积分方程 (BSVIEs) 对于模拟复杂的金融场景,如时间不一致和路径依赖偏好至关重要.
  • 现有的方法与BSVIEs固有的二维时间结构和复杂的依赖关系作斗争.

研究的目的:

  • 为BSVIEs及其反映的扩展开发一个强大的数值近似框架.
  • 在产品概率空间中为BSVIEs建立一个有利位置和可测量的基础.
  • 将基于深度学习的倒向随机微分方程 (BSDE) 解决方案扩展到 BSVIE 设置.

主要方法:

  • 开发了BSVIE定位性和可测量的框架,使用一个参数化的逆向随机方程家族.
  • 引入了一种离散时间学习方案,将哈马古奇-塔古奇离散化与深度神经网络相结合.
  • 一般化深度BSDE解决器技术,以解决BSVIEs的二维时间结构.

主要成果:

  • 建立了一个严格的对拟议的深度学习方案的融合分析,应用于BSVIEs.
  • 成功扩展了数值解析器来处理反射BSVIEs,使得在延迟递归公用事业等领域的应用成为可能.
  • 证明了该方法在接近复杂金融模型的解决方案中的有效性.

结论:

  • 拟议的深度学习方法为解决BSVIEs及其反映变体提供了一种有效和准确的数值方法.
  • 这项工作弥合了理论BSVIE框架和实际计算解决方案之间的差距.
  • 这些发现对定量金融有重大影响,特别是在模拟递归公用事业和具有记忆效应的金融衍生工具方面.