MATH5975随机分析

现代金融市场理论依赖于先进的数学和统计方法用于对复杂金融交易中的风险进行建模、预测和管理。之后1973年发表了Black和Scholes关于套利定价的突破性论文欧洲看涨期权，很明显，随机分析是一个不可或缺的工具金融市场理论，标准期权、奇异期权和其他衍生产品价格的推导证券，对冲相关金融风险，以及管理利率风险MATH5975Introduction to Stochastic Analysis
Please visit the School of Mathematics and Statistics website for a range of information on SchoolPolicies, Forms and Help for Students.
For information on Courses, please go to “Current Students” and either Undergraduate and/orPostgraduate”, Course Homepage” for

1.Course Aims

Modern theory of financial markets relies on advanced mathematical and statistical methods thatare used to model, forecast and manage risk in complex financial transactions. After thepublication in 1973 of the ground-breaking paper of Black and Scholes on the arbitrage pricing ofEuropean call options, it became clear that Stochastic Analysis is an indispensable tool for thetheory of financial markets, derivation of prices of standard and exotic options and other derivativesecurities, hedging related financial risk, as well as managing the interest rate risk.In this course, you will learn the basic concepts and techniques of Stochastic Analysis, such as:Brownian motion, martingales, Ito stochastic integral, Ito's formula, stochastic differentialequations, equivalent change of a probability measure, integral representation of martingales withrespect to a Brownian filtration, relations to second order partial differential equations, theFeynman-Kac formula, and stochastic processes with discontinuities.The course consists of theorems and proofs. The main goal of the course is to provide anecessary mathematical background for MATH5816 Continuous Time Financial Modelling andMATH5985 Term Structure Modelling, rather than to focus directly on financial concepts.

2.Course Description

Modern theory of financial markets relies on advanced mathematical statistical methods that areused to model, forecast and manage risk in complex financial transactions. After publication in1973 of the ground-breaking paper of Black and Scholes on the arbitrage pricing of European calloptions, Stochastic Analysis became an indispensable tool for the theory of financial markets,derivation of prices of standard and exotic options and other derivative securities, hedging relatedfinancial risk, as well as managing the interest rate risk. In this course, you will learn the basicconcepts and techniques of Stochastic Analysis, such as: Brownian motion, Ito stochastic integral,Ito's formula, changes of measures, stochastic differential equations, and their relations to secondorder partial differential equations, and Feynman-Kac formula.Assessment Week Weighting%
Due date if applicable Course LearningOutcome (CLO)Assignment 1 Week 4 5% Due week 4 CLO1, CLO2, CL03Midterm Test Week 7 20% Due week 7 CLO1, CLO2, CLO3Assignment 2 Week 10 15% Due week 10 CLO1, CLO2, CLO3Final Exam 60% UNSW Exam Period AllLate Submission of Assessment TasksNo late submissions will be accepted. (Where "late" in this context means after any extensionsgranted for Special Consideration or Equitable Learning Provisions.)Course Learning Outcomes (CLO)1. Recognise which analysis procedure is appropriate for a given research problem.2. Apply probability theory and stochastic analysis to practical problems.3. Demonstrate an understanding of the usefulness of Stochastic Analysis in yourprofessional area.

3.Course Schedule

The course will include material taken from some of the following topics. This is should only serveas a guide as it is not an extensive list of the material to be covered and the timings areapproximate. The course content is ultimately defined by the material covered in lectures; refer toMoodle for Lecture notes.Weeks Topic1 Basic Probability, Conditional Expectation2 Stopping Times, Discrete Time Martingales3 Continuous Time Martingale, Brownian Motion,4 Stochastic Log in to Moodle to find announcements, general information, notes,
The School of Mathematics and Statistics has adopted a number of policies relating to enrolment,attendance, assessment, plagiarism, cheating, special consideration etc. These are in addition tothe Policies of The University of New South Wales. Individual courses may also adopt otherpolicies in addition to or replacing some of the School ones. These will be clearly notified in theCourse Initial Handout and on the Course Home Pages on the Maths Stats web site.
Students in courses run by the School of Mathematics and Statistics should be aware of the Schooland Course policies by reading the appropriate pages on the Maths Stats web site starting at:https://www.maths.unsw.edu.au/currentstudents/assessment-poli...
The School of Mathematics and Statistics will assume that all its students have read andunderstood the School policies on the above pages and any individual course policies on theCourse Initial Handout and Course Home Page. Lack of knowledge about a policy will not be anexcuse for failing to follow the procedure in it.Academic Integrity and PlagiarismUNSW has an ongoing commitment to fostering a culture of learning informed by academicintegrity. All UNSW staff and students have a responsibility to adhere to this principle of academicintegrity. Plagiarism undermines academic integrity and is not tolerated at UNSW. Plagiarism atUNSW is defined as using the words or ideas of others and passing them off as your own.The UNSW Student Code provides a framework for the standard of conduct expected of UNSWstudents with respect to their academic integrity and behaviour. It outlines the primaryPage | 6obligations of students and directs staff and students to the Code and related procedures.In addition, it is important that students understand that it is not permissible to buyessay/writing services from third parties as the use of such services constitutes plagiarismbecause it involves using the words or ideas of others and passing them off as your own. Nor isit permissible to sell copies of lecture or tutorial notes as students do not own the rights to thisintellectual property.If a student breaches the Student Code with respect to academic integrity, the University may takedisciplinary action under the Student Misconduct Procedure.The UNSW Student Code and the Student Misconduct Procedure can be found at:https://student.unsw.edu.au/plagiarism
An online Module “Working with Academic Integrity” (https://student.unsw.edu.au/aim) is a six-lesson interactive self-paced Moodle module exploring and explaining all of these terms andplacing them into your learning context. It will be the best one-hour investment you’ve ever made.

4.Plagiarism

Plagiarism is presenting another person's work or ideas as your own. Plagiarism is a seriousbreach of ethics at UNSW and is not taken lightly. So how do you avoid it? A one-minute video foran overview of how you can avoid plagiarism can be ELISE (Enabling Library and Information Skills for Everyone)ELISE is designed to introduce new students to studying at UNSW.Completing the ELISE tutorial and quiz will enable you to:analyse topics, plan responses and organise research for academic writing and otherassessment tasks effectively and efficiently find appropriate information sources and evaluate relevanceto your needsuse and manage information effectively to accomplish a specific purposePage | 7better manage your time
understand your rights and responsibilities as a student at UNSW be aware of plagiarism, copyright, UNSW Student Code of Conduct and Acceptable Use ofUNSW ICT Resources Policybe aware of the standards of behaviour expected of everyone in the UNSW community locate services and information about UNSW and UNSW LibrarySome of these areas will be familiar to you, others will be new. Gaining a solid understanding of allthe related aspects of ELISE will help you make the most of your studies at UNSW.The ELISE training webpages:https://subjectguides.library.unsw.edu.au/elise/aboutelise
Equitable Learning Services (ELS)If you suffer from a chronic or ongoing illness that has, or is likely to, put you at a seriousdisadvantage, then you should contact the Equitable Learning Services (previously known asSEADU) who provide confidential support and advice.They assist students:living with disabilities with long- or short-term health concerns and/or mental health issues who are primary carers from low SES backgrounds of diverse genders, sexes and sexualitiesfrom refugee and refugee-like backgrounds from rural and remote backgrounds who are the first in their family to undertake a bachelor-level degree.Equitable Learning Services (ELS) may determine that your condition requires specialarrangements for assessment tasks. Once the School has been notified of these, we will makeevery effort to meet the arrangements specified by ELS.Additionally, if you have suffered significant misadventure that affects your ability to complete thecourse, please contact your Lecturer-in-charge in the
Academic Skills Support and the Learning CentreThe Learning Centre offers academic support programs to all students at UNSW Australia. Weassist students to develop approaches to learning that will enable them to succeed in theiracademic study. For further information on these programs please go to:http://www.lc.unsw.edu.au/services-programsApplications for Special Consideration for Missed Assessment
Please adhere to the Special Consideration Policy and Procedures provided on the web pagebelow when applying for specialconsideration.https://student.unsw.edu.au/special-considerationPlease note that the application is not considered by the Course Authority, it is considered by acentralised team of staff at the Nucleus Student Hub.The School will contact you (via student email account) after special consideration has beengranted to reschedule your missed assessment, for a lab test or paper-based test only.For applications for special consideration for assignment extensions, please note that the newsubmission date and/or outcome will be communicated through the special consideration website only, no communication will be received from the School.
For Dates on Final Term Exams and Supplementary Exams please check the “Key Dates forExams” ahead of time to avoid booking holidays or work obligations.https://student.unsw.edu.au/exam-datesIf you believe your application for Special Consideration has not been processed, you should [e-mail] immediately for advice.Course Evaluation and Development (MyExperience)Student feedback is very important to continual course improvement. This is demonstrated withinthe School of Mathematics and Statistics by the implementation of the UNSW online studentPage | 9survey myExperience, which allows students to evaluate their learning experiences in ananonymous way. myExperience survey reports are produced for each survey. They are released tostaff after all student assessment results are finalised and released tostudents.Courseconvenor will use the feedback to make ongoing improvements to the course.
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