財務數學導論(TW交通大學)

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財務數學導論(一) Introduction to Financial Mathematics I http://ocw.nctu.edu.tw/course_de ... id=187#.WHmVNxt942y

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

財務數學導論(二) Introduction to Financial Mathematics II

單元	課程內容
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

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