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 在 1973 年 Fisher Black 和 Myron Scholes利用熱能替換公式推導出選擇權評價公式的解。但是它只用在完美市場的情況下。所以我們利用 Fourierseries的概念，給此原方程一個有固定震盪頻率的外力，以 sine 級數來表示在某個時間點有人想抬高股票價格，但又在某些時間點有另外的一批人想壓低股價，導致市場上股價一直有上下波動的情況發生。最後再探討我們有外力的選擇權價格的解和 Black-Scholes原方程的解之間的不同。
 In 1973, Fisher Black and Myron Scholes solved the options valuedformula with the Heat Exchange Equations. But it is used in a perfect market.We use the concept of Fourier series to express an oscillation by outer forcefor the original equation. Using the sine series, it represents that some personwants to raise the stock price in some time, but some other people want to reducethe stock price in certain time. Therefore the stock price undulation alwaysoccurs in the market. Finally, we discuss the difference of the solutionsof the option price with outer force and the Black-Scholes originalequation.
 1. Introduction2. Fundations and Results 2.1 Heat Equation 2.2 The Schwartz Space 2.3 The Fourier Series 2.4 The Fourier Transform 2.5 Tempered Distributions 2.6 The Homogenous and Non-homogenous Black-Scholes Model 2.7 The Convergence of solutions in the space of distribution
 [1] G. Barles and H. M. Soner, Option pricing with transactioncosts and a nonlinear Black-Scholes equation, Finance Stochast. 2 (1998)369-397.[2]F. Black and M. Scholes, The price of options andcorporate liabilites, Journal of Political Economy ,81 (1973),637-659.[3] P. Boyle and T. Vorst, Option replication in discrete timewith transaction costs, J. Finance. 47 (1992) 271-293.[4] M. Davis, V. Panis and T. Zariphopoulou, European optionpricing with transaction fees, SIAM J. Contr. Optim. 31 (1993) 470-493.[5] J. Dewynne, S. Howison and P. Wilmott, Option Pricing:Mathematical Models and Computation (Oxford, Financial Press, 1995).[6] R. Frey, Perfect option hedging for a large trader,Finance Stochast. 2 (1998) 115-141.[7] R. Frey, Market illiquidity as a source of model risk indynamic hedging, in Model Risk, R. Gibson, ed. (RISK Publications, London,2000).[8] G. Genotte and H. Leland, Market liquidity, hedging andcrashes, Amer. Econ. Rev. 80 (1990) 999-1021.[9] R. Jarrow, Market manipulation, bubbles,corners and shortsqueezes, j. Financial Quant. Anal. 27 (1992) 311-336.[10] J. Leitner, Continuous time CAPM, price for risk andutility maximization, in Mathematical Finance, M. Kohlmann et al.ed.Workshop of the Mathematical Finance Research Project, Konstanz, Germany(Birkh\"{a}user, Basel, 2001).[11]R. C. Merton, Theory of rational option pricing, Bell J.Econ. Manag. Sci. 4 (1973) 141-183.[12]E. Platen and M. Schweizer, On feedback effects fromhedging derivatives, Math. Finance. 8 (1998) 67-84.[13]P. Sch\"{o}nbucher and P. Wilmott, The feedback effect ofhedging in illiquid mackets, SIAM J. Appl. Math. 61 (2000) 232-272.[14] John Hull, Options, Futures, and other Derivatives,ch11\$\sim\$ ch12.[15]Jeffrey Rauch, Partial Differential Equations, ch2\$\sim\$ch3.[16] Stanley J. Farlow, Partial Differential Equations for Scientists and Engineers.[17]陳宏,郭震坤, 財務數學(上),數學傳播季刊,第26卷第1期,中央研究院數學研究所發行.[18]陳宏,郭震坤, 財務數學(下),數學傳播季刊,第26卷第2期,中央研究院數學研究所發行.
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 1 應用傅立葉級數預測雲林科技大學圖書館用電量 2 應用改良式傅立葉級數預測建築物用電量

 1 [18]陳宏,郭震坤, 財務數學(下),數學傳播季刊,第26卷第2期,中央研究院數學研究所發行. 2 [17]陳宏,郭震坤, 財務數學(上),數學傳播季刊,第26卷第1期,中央研究院數學研究所發行.

 1 台指選擇權賣出勒式策略分析 2 選擇權和現貨市場非同步交易時段所隱含的資訊之探討 3 選擇權未平倉量與加權股價指數之相關性探討 4 控制變異與HaltonSequences蒙地卡羅之臺指選擇權模擬 5 股票與選擇權市場的價格發現與資訊交易之探討－以台灣股價指數為例 6 選擇權評價之有限差分外插法 7 Black-Scholes方程式的數值模擬與選擇權定價問題之相關應用 8 資訊不對稱下，股票與選擇權知訊交易策略之研究 9 台灣股價指數選擇權套利機會之實證研究 10 台指選擇權隱含波動幅度型態之實證研究 11 台指選擇權機率密度函數之定價分析與避險衡量 12 選擇權價格預測與設定報酬率策略操作之實證研究 13 台指期貨、台指選擇權策略之績效分析-以做多策略為例 14 利用快速傅立葉轉換進行跳躍發散與隨機波動模型之選擇權評價應用—以台指選擇權為例 15 外匯期貨選擇權定價-VG與FFT方法

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