Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/141183
題名: 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
作者: 方麒豪
Fang, Chi-Hao
貢獻者: 許順吉<br>林士貴
Sheu, Shuenn-Jyi<br>Lin, Shih-Kuei
方麒豪
Fang, Chi-Hao
關鍵詞: 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
Neural Networks
Finite Difference
Merton PIDE
Black-Scholes PDE
European Call Option Price
日期: 2022
上傳時間: 1-Aug-2022
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。
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.
參考文獻: Cont, R., & Voltchkova, E. (2006). A finite difference scheme for option pricing in jump\ndiffusion and exponential lévy models. SIAM Journal on Numerical Analysis, 43(4),\n1596–1626. https://doi.org/10.1137/S0036142903436186\nCybenko, G. (1989). Approximation by superpositions of a sigmoidal function. Mathematics of\nControl, Signals, and Systems, 2, 303–314. https://doi.org/10.1007/BF02551274\nLeshno, M., Lin, V. Y., Pinkus, A., & Schocken, S. (1993). Multilayer feedforward networks\nwith a nonpolynomial activation function can approximate any function. Neural\nNetworks, 6(6), 861–867. https://doi.org/10.1016/S0893-6080(05)80131-5\nLu, L., Meng, X., Mao, Z., & Karniadakis, G. E. (2021). Deepxde: A deep learning library for\nsolving differential equations. SIAM Review, 63(1), 208–228. https://doi.org/10.1137/\n19M1274067\nRaissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A\ndeep learning framework for solving forward and inverse problems involving nonlinear\npartial differential equations. Journal of Computational Physics, 378(1), 686–707. https:\n//doi.org/10.1016/j.jcp.2018.10.045\nSchwartz, E. (1977). The valuation of warrants: Implementing a new approach. Journal of\nFinancial Economics, 4, 79–93. https://doi.org/10.1016/0304-405X(77)90037-X\n30
描述: 碩士
國立政治大學
應用數學系
109751007
資料來源: http://thesis.lib.nccu.edu.tw/record/#G0109751007
資料類型: thesis
Appears in Collections:學位論文

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