財務數學導論(二) Introduction to Financial Mathematics II | 應用數學系吳慶堂老師

Introduction to Financial Mathematics II

財務數學導論(二)

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本課程是由交通大學應用數學系提供。
本課程主要讓學生了解並熟悉研究財務金融方面所需之數學工具。

課程用書：S. E. Shreve: Stochastic Calculus for Finance II: Continuous-Time Models, Springer, 2004.

參考用書：

T. M. Apostol: Mathematical Analysis, Second Edition
M. Baxter and A. Rennie: Financial Calculus.
T. Björk: Arbitrage Theory in Continuous Time.
K. L. Chung: A Course in Probability Theory, Second Edition.
F. Delbaen and W. Schachermayer: The Mathematics of Arbitrage.
J. Elstrodt: Maβ- und Integrationstheorie, Third Edition.
H. Föllmer and A. Schied: Stochastic Finance. An Introduction in Discrete Time.
J. Jacod and Ph. Protter: Probability Essentials.
J. C. Hull: Options, Futures, & Other Derivatives, Sixth Edition.
I. Karatzas: Lectures on the Mathematics of Finance.
I. Karatzas and S. E. Shreve: Brownian Motion and Stochastic Calculus, Second Edition.
I. Karatzas and S. E. Shreve: Method of Mathematical Finance.
D. Lamberton and B. Lapeyre: Introduction to Stochastic Calculus Applied to Finance.
B. Øksendal: Stochastic Differential Equations, An Introduction with Applications,Sixth Edition.
R. T. Rockafellar: Convex Analysis.
H. L. Royden: Real Analysis, Third Edition.
A.N. Shiryaev: Probability Theory, Second Edition.
S. E. Shreve: Stochastic Calculus for Finance I: The Binomial Asset Pricing Model.
R. L. Wheeden and A. Zygmund: Measure and integral.

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授課教師	應用數學系吳慶堂老師
課程學分	3學分
授課年度	99學年度
授課對象	碩士班學生
預備知識	微積分
課程提供	課程影音課程綱要課程行事曆

每頁顯示個資料列

搜尋:

週次	課程內容	課程影音
	單元七 Coutinuous-time Martingales 7.1 Stochastic process (1/2)	線上觀看
	7.1 Stochastic process (2/2)	線上觀看
	7.2 Uniform integrability	線上觀看
	7.3 Martingale theory in continuous-time	線上觀看
	7.4 Local martingales	線上觀看
	7.5 Doob-Meyer decomposition	線上觀看
	7.6 Semimartingales	線上觀看
	單元八 Brownian Motions 8.1 Scaled random walk	線上觀看
	8.2 Brownian motions	線上觀看
	8.3 The Brownian sample paths	線上觀看
	8.4 Exponential martingales	線上觀看
	8.5 d-dimensional Brownian motions	線上觀看
	單元九 Stochastic Integrals 9.1 Construction of stochastic integrals with respect to martingales (1/3)	線上觀看
	9.1 Construction of stochastic integrals with respect to martingales (2/3)	線上觀看
	9.1 Construction of stochastic integrals with respect to martingales (3/3)	線上觀看
	9.2 Stochastic integrals with respect to semimartingales	線上觀看
	9.3 Stochastic integrals with respect to local martingales	線上觀看
	9.4 Itô formula (1/2)	線上觀看
	9.4 Itô formula (2/2)	線上觀看
	9.5 Integration by parts	線上觀看
	9.6 Martingale representation theorem	線上觀看
	9.7 Change of Measures	線上觀看
	9.8 Girsanov theorem	線上觀看
	9.9 Local times	線上觀看
	單元十 Stochastic Differential Equations 10.1 Examples and some solution methods (1/2)	線上觀看
	10.1 Examples and some solution methods (2/2)	線上觀看
	10.2 An existence and uniqueness result	線上觀看
	10.3 Weak and strong solutions	線上觀看
	10.4 Feynman-Kac theorem	線上觀看
	單元十一 Continuous-Time Models 11.1 Market portfolios and arbitrage	線上觀看
	11.2 Equivalent local martingale measures	線上觀看
	11.3 Completeness	線上觀看
	11.4 Pricing for attainable contingent claim	線上觀看
	11.5 Black-Scholes-Merton formula	線上觀看
	11.6 The Greeks	線上觀看
	11.7 Parity rrelations	線上觀看
	單元十二 Hedging 12.1 Hedging strategy for the simple contingent claim 12.2 Delta and gamma hedging	線上觀看
	Appendix F、Characteristic Functions	線上觀看
	Appendix G、Differntial Equations	線上觀看
	Appendix H、Convex Analysis	線上觀看

目前顯示第 1 至第 40 個資料列，總計 40 個資料列

課程目標

本課程主要讓學生了解並熟悉研究財務金融方面所需之數學工具。

課程章節

章節	主題內容
單元七 Continuous-Time Martingales	7.1 Stochastic processes 7.2 Uniform integrability 7.3 Martingale theory in continuous-time 7.4 Local martingales 7.5 Doob-Meyer decomposition 7.6 Semimartingales
單元八 Brownian Motions	8.1 Scaled random walk 8.2 Brownian motions 8.3 The Brownian sample paths 8.4 Exponential martingales 8.5 d-dimensional Brownian motions
單元九 Stochastic Integrals	9.1 Construction of stochastic integrals with respect to martingales 9.2 Stochastic integrals with respect to semimartingales 9.3 Itô formula 9.4 Integration by parts 9.5 Martingale representation theorem 9.6 Girsanov theorem 9.7 Local times
單元十 Stochastic Differential Equations	10.1 Examples and some solution methods 10.2 An existence and uniqueness result 10.3 Weak and strong solutions 10.4 Feynman-Kac theorem
單元十一 Continuous-Time Models	11.1 Market portfolios and arbitrage 11.2 Equivalent local martingale measures 11.3 Completeness 11.4 Pricing for attainable contingent claim 11.5 Black-Scholes-Merton formula 11.6 Parity relations 11.7 The greeks
單元十二 Hedging	12.1 Hedging strategy for the simple contingent claim 12.2 Delta and gamma hedging 12.3 Superhedging 12.4 Quantile hedging
單元六 Volatility	13.1 Historical volatility 13.2 Implied volatility
Appendix	F . Convex Analysis

課程書目

S. E. Shreve: Stochastic Calculus for Finance II: Continuous-Time Models, Springer, 2004.

參考書目

T. M. Apostol: Mathematical Analysis, Second Edition
M. Baxter and A. Rennie: Financial Calculus.
T. Björk: Arbitrage Theory in Continuous Time.
K. L. Chung: A Course in Probability Theory, Second Edition.
F. Delbaen and W. Schachermayer: The Mathematics of Arbitrage.
J. Elstrodt: Maβ- und Integrationstheorie, Third Edition.
H. Föllmer and A. Schied: Stochastic Finance. An Introduction in Discrete Time.
J. Jacod and Ph. Protter: Probability Essentials.
J. C. Hull: Options, Futures, & Other Derivatives, Sixth Edition.
I. Karatzas: Lectures on the Mathematics of Finance. I. Karatzas and S. E. Shreve: Brownian Motion and Stochastic Calculus, Second Edition.
I. Karatzas and S. E. Shreve: Method of Mathematical Finance.
D. Lamberton and B. Lapeyre: Introduction to Stochastic Calculus Applied to Finance.
B. Øksendal: Stochastic Differential Equations, An Introduction with Applications,Sixth Edition.
R. T. Rockafellar: Convex Analysis.
H. L. Royden: Real Analysis, Third Edition.
A.N. Shiryaev: Probability Theory, Second Edition.
S. E. Shreve: Stochastic Calculus for Finance I: The Binomial Asset Pricing Model.
R. L. Wheeden and A. Zygmund: Measure and integral.

評分標準

項目	百分比
平時成績(作業)	40%
期中考	30%
期末考	30%

本課程行事曆提供課程進度與考試資訊參考。

章節	主題內容
單元七 Continuous-Time Martingales	7.1 Stochastic processes 7.2 Uniform integrability 7.3 Martingale theory in continuous-time 7.4 Local martingales 7.5 Doob-Meyer decomposition 7.6 Semimartingales
單元八 Brownian Motions	8.1 Scaled random walk 8.2 Brownian motions 8.3 The Brownian sample paths 8.4 Exponential martingales 8.5 d-dimensional Brownian motions
單元九 Stochastic Integrals	9.1 Construction of stochastic integrals with respect to martingales 9.2 Stochastic integrals with respect to semimartingales 9.3 Itô formula 9.4 Integration by parts 9.5 Martingale representation theorem 9.6 Girsanov theorem 9.7 Local times
單元十 Stochastic Differential Equations	10.1 Examples and some solution methods 10.2 An existence and uniqueness result 10.3 Weak and strong solutions 10.4 Feynman-Kac theorem
單元十一 Continuous-Time Models	11.1 Market portfolios and arbitrage 11.2 Equivalent local martingale measures 11.3 Completeness 11.4 Pricing for attainable contingent claim 11.5 Black-Scholes-Merton formula 11.6 Parity relations 11.7 The greeks