and Advanced Mathematical Finance

**Section 001**

* 11:30 - 12:20 MWF*

**Fall Semester, 2010**

3 credit hours

The course goals are:

- Understand the properties of stochastic processes such as
sequences of random variables, coin-flipping games,
Brownian motion and the solutions of stochastic differential equations as
a means for modeling modern financial instruments for the management of risk.
- Use sophisticated financial instruments for the management of risk
as motivations for the detailed study
of stochastic processes and solutions of stochastic
differential equations.
- One emphasis will be on understanding standard
stochastic processes at the level of the classic references by Karlin
and Taylor, and Feller. The course will not hesitate to prove
mathematical statements at the level of proof employed in Math 325.
- The course emphasizes the mathematical modeling process
applied to a modern area which is not based on physical science yet
still leads to classical partial differential equations and numerical
methods. The field of mathematical finance is only 35 years old, uses
leading-edge mathematical and economic ideas, and has some
controversial foundational hypotheses. Mathematical finance is also
data-rich and even advanced results are testable in the market. Using
mathematics illustrated daily on
newspaper financial pages, the course applies the full cycle
of mathematical modeling and analysis in a non-trivial,
but still accessible, way that has economic implications.
- The goal of the course will be to reach a point where the students thoroughly understand the derivation and modeling of financial instruments, advanced financial models, advanced stochastic processes, partial differential equations, and numerical methods at a level sufficient for beginning graduate study in mathematics, finance, economics, actuarial science, and for entry-level positions in the sophisticated financial services industry.

*ACE Outcome 10:* This course satisfies ACE Outcome 10. The
entire set of your homework, projects and exams will be a scholarly product
that requires broad knowledge, appropriate technical proficiency,
information collection, synthesis, interpretation, presentation, and
reflection.

The course provides a capstone mathematical experience in that it combines the mathematical areas of probability and statistics, mathematical modeling, calculus, difference and differential equations, numerical solution and simulation and mathematical analysis in a single course. In addition, the course uses all of these topics to investigate modern financial instruments that have enormous economic influence, but are hidden from popular view because they are wrongly believed to be esoteric and difficult. The course is based on material that is extremely data-rich. The financial news has daily coverage of price fluctuations, not to mention Internet resources which can provide nearly real-time as well as historical coverage of financial information. This provides the opportunity for students to compare the theoretical understanding to the reality of financial markets. The combination of these topics gives the course a unified view of mathematics in the context of an important modern application.

Keep a file of your graded projects and exams. To satisfy Outcome 10, some of these files will be collected, copied and returned at the end of the course.

The technical prerequisites of the seminar are understanding of

- the meaning and calculation of mean, variance, and standard deviation
- calculating joint probabilities of independent events,
- the meaning and use of binomial random variables,
- the meaning and calculation of probabilities for a normal random variable.

The class will meet Fall Semester 2010, 11:30 - 12:20, Mondays, Wednesdays, and Fridays.

The text for the course will be published on the web at
` http://www.math.unl.edu/~sdunbar1/Teaching/MathematicalFinance/`

` mathfinance.shtml`

and also on the UNL Blackboard site: `my.unl.edu` in the course
`STOCHASTIC PROCESSES MATH489 SEC001 FALL 2010`. Students will
need access to a web-browser capable of rendering MathML. I recommend
the freely available
Firefox 3.5 or later, available for all platforms. Students may also need to occasionally
use specialized mathematical software in the Mathematics Computer Lab,
Avery 18. Students registered for a math class automatically a valid
log-in for the Mathematics Computer Lab.

**Office and Availability:**

Office Hours: Mon-Wed-Fri, 10:30 am - 11:20 am, 308 Avery

Phone: 472-7236 (24 hour University Voice Mail)

Math Department: 472-3731 (8:00 AM - 5:00 PM)

Email: ` sdunbar1@unl.edu `

, URL: ` http://www.math.unl.edu/~sdunbar1 `

**Class Policies:**

- Collaboration on homework is allowed, but each student must turn in the assigned homework.
- Grading will be based on approximately 10 homework assignments worth approximately 47%, quizzes worth approximately 15%, an extended project worth 13%, one mid-term exam worth approximately 15%, and one comprehensive final exam worth approximately 15% of the course grade.
- The mid-term is tentatively scheduled for class time Friday, October 29, 2010 and the Final Exam is scheduled for 10:00 AM - 12:00 NOON, Tuesday, Dec 14, 2010.

and Advanced Mathematical Finance

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**LaTeX**2`HTML` translator Version 2002-2-1 (1.71)

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Nikos Drakos,
Computer Based Learning Unit, University of Leeds.

Copyright © 1997, 1998, 1999,
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Mathematics Department, Macquarie University, Sydney.

The command line arguments were:

**latex2html** `prospectus10.tex`

The translation was initiated by Steven Dunbar on 2010-08-19

Department of Mathematics and Statistics

University of Nebraska-Lincoln

Lincoln, NE, 68588-0323 USA

email: sdunbar@math.unl.edu

Steve Dunbar's Home Page