臺灣博碩士論文加值系統

本論文以Black-Scholes equation為基本模型，論文中先用基本的方法，探討在有外力的市場中，歐式買權價格的改變。
並且在相同的情況下，再用Mellin transform當工具來探討比較，以突顯Mellin transform的方便性。進一步，更利用Mellin transform的方法
探討常數外力，固定不變的外力等情況，透過數學式子試著說明外力對歐式買權價格的影響。
這些的外力情形就像是路障干擾一樣，會導致歐式買權價格在某個時間點受到影響而改變。

We take Black-Scholes equation as the basic model. In this paper, we use the fundamental method to study European call
option price in a non-ideal market. In the same situation, we also use Mellin transform as the study tool.
Moreover, we use Mellin transform to study the equation of the European call option price with outside forces.
With a mathematical explanation, the influences of the outer force on European option price are systematically solved.
These outside forces are similar to bumper interruptions. They can induce the European call option price change at some time.

摘要 i
Abstract ii
謝辭 iii
1 Introduction 1
1.1 Study Motivation and Background ……………………………… 1
1.2 Study Range and Goal ………………………………………………… 4
1.3 Study Method …………………………………………………………… 6
2 Tools Use in This Research 7
2.1 Heat Equation …………………………………………………………… 7
2.2 Schwartz Space ………………………………………………………… 8
2.3 Tempered Distribution ………………………………………………… 9
2.4 Mellin transform ……………………………………………………… 10
2.5 Author’s Theorem ……………………………………………………… 11
3 Prove of Theorem 14
3.1 Proof of Theorem 2.5.1 ………………………………………………14
3.2 Proof of Theorem 2.5.3 ………………………………………………22
3.3 Proof of Theorem 2.5.5 …………………………………………… 28
3.4 Proof of Theorem 2.5.6 ……………………………………………… 33
3.5 Proof of Theorem 2.5.7 ……………………………………………… 35
4 Applications and Futher Study 38
4.1 Conclusions of Theorem 2.5.1 …………………………………… 38
4.2 Conclusions of Theorem 2.5.3 …………………………………… 39
4.3 Conclusions of Theorem 2.5.5 …………………………………… 39
4.4 Conclusions of Theorem 2.5.6 …………………………………… 41
4.5 Conclusions of Theorem 2.5.6 …………………………………… 42
4.6 Summary of This Paper ……………………………………………… 45
References 46

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