空间-时间分数Black-Scholes方程的自由边界问题的最佳近似方法是使用结合物理信息的神经网络
Lina Song1, Yousheng Tan2, Fajun Yu3
1School of Data Science and Artificial Intelligence, Dongbei University of Finance and Economics, 116025, Dalian, China. l_n_song@163.com.
Scientific reports
|October 25, 2024
概括
这项研究使用物理信息的神经网络来解决美国抛售期权定价的分数Black-Scholes方程. 研究结果表明,分数计算和神经网络提供了更现实的市场预测.
科学领域:
- 计算金融是指计算金融.
- 应用数学 应用数学 应用数学
- 机器学习 机器学习
背景情况:
- 分数Black-Scholes方程提出了复杂的自由边界问题.
- 传统模型可能无法完全捕捉金融波动中的长期记忆效应.
- 美国期权定价需要复杂的数值方法.
研究的目的:
- 开发一种新的方法来解决分数Black-Scholes方程中的自由边界问题.
- 调查不同分数衍生品 (卡普托,卡普托-法布里齐奥,阿坦加纳-巴莱努-卡普托) 对期权定价的影响.
- 用先进的计算技术来增强美国 Put 期权定价的现实性.
主要方法:
- 设计了一个联合物理信息神经网络 (PINN) 架构,结合了转移学习和数据增强层.
- 应用PINN来数量解决经典和分数Black-Scholes模型.
- 进行了实证分析,模拟了美国抛售期权的最佳行使边界.
主要成果:
- 该研究成功地解决了空间-时间分数Black-Scholes方程的自由边界问题.
- 对比分析表明,拟议的神经网络方法的有效性.
- 引入微积分和神经网络,为美国的抛售期权定价带来了更现实的预测结果.
结论:
- 结合PINN方法提供了一个可行的方法来定价美国期权用微积分计算.
- 这项研究为未来的研究提供了坚实的框架,结合了分数计算,神经网络和市场数据.
- 该方法可以扩展到解决其他科学领域的自由边界问题.
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