定 價(jià)：67 元
叢書(shū)名：美國(guó)數(shù)學(xué)會(huì)經(jīng)典影印系列
- 作者：R.J.Williams 著
- 出版時(shí)間：2017/1/1
- ISBN：9787040469127
- 出 版 社：高等教育出版社
- 中圖法分類：F830
- 頁(yè)碼：150
- 紙張：膠版紙
- 版次：1
- 開(kāi)本：16開(kāi)
自三十多年前Black和Scholes的開(kāi)創(chuàng)性工作出現(xiàn)以來(lái)，金融數(shù)學(xué)這個(gè)現(xiàn)代學(xué)科無(wú)論在理論還是實(shí)踐方面都經(jīng)歷了巨大發(fā)展�！督鹑跀�(shù)學(xué)引論（英文版）》旨在介紹部分基礎(chǔ)理論，使得學(xué)生和研究人員了解后能夠閱讀更高級(jí)的教科書(shū)和研究文章。
《金融數(shù)學(xué)引論（英文版）》一開(kāi)始討論了歐式和美式衍生產(chǎn)品在離散二叉樹(shù)模型（即離散時(shí)間和離散狀態(tài)）下套期保值和定價(jià)的基本思想的發(fā)展，然后介紹了一個(gè)一般的離散有限市場(chǎng)模型，并在此場(chǎng)合中證明了資產(chǎn)定價(jià)的一些基本定理。概率論中的諸如條件期望、濾波、（超）鞅、等價(jià)鞅測(cè)度、鞅表示等工具，在這個(gè)簡(jiǎn)單的離散框架下被首次用到，從而搭建了通向連續(xù)（時(shí)間和狀態(tài)）場(chǎng)合的橋梁，后者需要布朗運(yùn)動(dòng)和隨機(jī)分析的概念。連續(xù)場(chǎng)合中*簡(jiǎn)單的模型是著名的Black-Scholes模型，歐式和美式衍生產(chǎn)品的定價(jià)和套期保值因此有所發(fā)展�！督鹑跀�(shù)學(xué)引論（英文版）》*后介紹了連續(xù)市場(chǎng)模型的一些基本定理，這個(gè)模型在多個(gè)方面推廣了簡(jiǎn)單Black-Scholes模型。
Preface
Chapter 1．Financial Markets and Derivatives
1．1．Financial Markets
1．2．Derivatives
1．3．Exercise
Chapter 2．Binomial Model
2．1．Binomial or CRR Model
2．2．Pricing a European Contingent Claim
2．3．Pricing an American Contingent Claim
2．4．Exercises
Chapter 3．Finite Market Model
3．1．Definition of the Finite Market Model
3．2．First Fundamental Theorem of Asset Pricing
3．3．Second Fundamental Theorem of Asset Pricing
3．4．Pricing European Contingent Claims
3．5．Incomplete Markets
3．6．Separating Hyperplane Theorem
3．7．Exercises
Chapter 4．Black-Scholes Model
4．1．Preliminaries
4．2．Black-Scholes Model
4．3．Equivalent Martingale Measure
4．4．European Contingent Claims
4．5．Pricing European Contingent Claims
4．6．European Call Option - Black-Scholes Formula
4．7．American Contingent Claims
4．8．American Call Option
4．9．American Put Option
4．10．Exercises
Chapter 5．Multi-dimensional Black-Scholes Model
5．1．Preliminaries
5．2．Multi-dimensional Black-Scholes Model
5．3．First Fundamental Theorem of Asset Pricing
5．4．Form of Equivalent Local Martingale Measures
5．5．Second Fundamental Theorem of Asset Pricing
5．6．Pricing European Contingent Claims
5．7．Incomplete Markets
5．8．Exercises
Appendix A．Conditional Expectation and LP-Spaces
Appendix B．Discrete Time Stochastic Processes
Appendix C．Continuous Time Stochastic Processes
Appendix D．Brownian Motion and Stochastic Integration
D．1．Brownian Motion
D．2．Stochastic Integrals (with respect to Brownian motion)
D．3．Ito Process
D．4．Ito Formula
D．5．Girsanov Transformation
D．6．Martingale Representation Theorem
Bibliography
Index
書(shū)單推薦
