標題: 財務數學導論（一）Introduction to Financial Mathematics I 作者: 吳慶堂開放教育推動中心Open Education Office 公開日期: 2010 摘要: 課程首頁 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。課程概述 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 單元 課程內容 課程介紹 單元一 Probability Theory 1.1 Probability space 1.2 Random variables 1.3 Expectation 單元二 Discrete-Time Martingales 2.1 Conditional probability and conditional expectation 2.2 Discrete time Martingales 2.3 Martingale transform and Doob decomposition 單元三 One-Period Model Introduction 3.1 Portfolios 3.2 Derivative securities 3.3 Absence of arbitrage 3.4 No arbitrage and price system 3.5 Martingale measures 3.6 Pricing 3.7 Complete market model 單元四 Multi-Period Model Introduction 4.1 The market model 4.2 Arbitrage opportunities 4.3 Martingale measures 4.4 Arbitrage-free prices for European contingent claim 單元五 American Contingent Claim 5.1 Stopping time 5.2 American claims 5.3 Arbitrage-free prices 單元六 Measures of Risk Introduction 6.1 Monetary measure of risk 6.2 Coherent and convex risk measures 6.3 Acceptance sets 6.4 Robust representation of coherent risk measure 6.5 Robust representation of convex risk measures Appendix A. Limits of Sequences of Numbers B. Convergence of Sequences of Functions and Stochastic Processes I C. Distribution Functions D. Convergence of Sequences of Functions and Stochastic Processes II E. Riemann-Stieltjes Integrals 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. Bjork: 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. Follmer 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. Oksendal: 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%授課對象：碩士班學生預備知識：微積分 URI: http://hdl.handle.net/11536/108269http://ocw.nctu.edu.tw/course_detail.php?bgid=1&nid=187 Appears in Collections: Open Course Ware