選擇權偏微分方程之數值分析: 有限差分法及類神經網路法之應用

Numerical Analysis of Option Partial Differential Equations: Applications of Finite Difference and Neural Networks Methods

方麒豪(Fang Chi-Hao)

指導教授 ： 許順吉 ； 林士貴

國立政治大學/理學院/應用數學系/碩士(2022年)

https://doi.org/10.6814/NCCU202201023

摘要

M. Raissi et al.(2019) 首先提出使用監督式學習方法用於求解偏微分方程。他們著重於有封閉解的偏微分方程並且使用封閉解與預測值的差距作為類神經網路的損失函數於訓練中。Lu et al.(2019) 提出更有效率的演算法用於求解多種類型的偏微分方程，包含正演問題以及反演問題。本文將著重於觀察歐式選擇權的類神經網路預測值行為與封閉解的差距並且跟有限差分法進行比較。

關鍵字

類神經網路 ； 有限差分法 ； Merton 偏積分微分方程 ； Black- Scholes 偏微分方程 ； 歐式選擇權價格

並列摘要

M. Raissi et al.(2019) first proposed a supervised learning method for solving partial differential equations. They focused on partial differential equations that have closed form solutions and used the difference between closed form solutions and neural network outputs as loss function for training. Lu et al.(2019) presented an efficient algorithm for solving several types of partial differential equations, including forward problem and inverse problems. This dissertation aims at observing the behaviour of European call option prices predicted by neural networks and comparing it with closed form price.

並列關鍵字

Neural Networks ； Finite Difference ； Merton PIDE ； Black-Scholes PDE ； European Call Option Price

參考文獻

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