《金融随机分析》马成虎

附件：大纲模板

研究生课程教学大纲

(Course Outline)

课程名称(Course Name in Chinese)：金融随机分析

英文名称(Course Name in English)：Stochastic Modeling in Finance

一、课程的教学目的(Course Purpose)

This course is an advanced treatment of no-arbitrage approach of stochastic modeling in finance. We shall put special emphasis on continuous time modeling. Fundamental theorem and various applications in option pricing and term structure of interest rates (TSIR) will be thoroughly covered.

二、教学内容及基本要求(T eaching Content and Requirements)

Topics include:

(a)Stochastic processes and stochastic calculus

(b)Trading strategy and market span

(c)No arbitrage and martingale pricing: The Fundamental Theorem

(d)Black-Scholes option pricing model

(e)Classical no arbitrage modeling on TSIR

(f)Heath-Jarrow-Morton’s approach on TSIR

(g)TSIR in presence of Levy jumps

三、考核方式及要求(Grading)

There will be no final examination. Students will be assessed on the basis of class participation, a mid-term test and a term paper.

Class participation 10%

Mid-term test 20%

Term paper 70%

Total 100%

四、学习本课程的前期课程要求(Required Courses in advance)

Asset Pricing, Econometrics/Statistics, Optimization

五、教材(Textbook)

马成虎：高级资产定价理论。中国人民大学出版社, 2010.

六、主要参考书目、文献与资料(Reading Materials)

1.Neftci S., An Introduction to the Mathematics of Financial Derivatives, 2nd edition. Academic

Press, 2000

2.Duffie D., Dynamic Asset Pricing Theory, 3rd Edition. Princeton University Press, 2001

七、具体教学安排(Detail Schedule)

Week 1-2Continuous time Stochastic Processes

∙Poisson process

∙Brownian motion

∙Levy measure and Poisson point process

∙Martingale and semi-martingale

References:

Ma (2010), Chapter 11 and extended references

Week 3-4Stochastic Differential Equations

∙Stochastic integral and stochastic differential equations

∙Ito’s lemma and Kolomogorov equation

∙Change of measure and Girsanov theorem

∙Examples

References:

Ma (2010), Chapter 11 and extended references

Week 5Fundamental theorem: continuous-time

∙Trading strategies and market span

∙No-arbitrage self-financing trading strategies

∙No-arbitrage and martingale representation of prices

References:

Ma (2010), Chapter 12

Delbaen F. and W. Schachermayer (1992), "Representing Martingale Measures when Asset Prices Are Continuous and Bounded", Mathematical Finance 2, 107-130.

Delbaen F. and W. Schachermayer (1994), "A General V ersion of the Fundamental Theorem of