link to University of Nebraska Lincoln
Department of Mathematics
203 Avery Hall
University of Nebraska Lincoln
Lincoln, NE 68588-0323
402-472-3731 (voice)
402-472-8466 (fax)

Math 489/Math 889
Stochastic Processes and
Advanced Mathematical Finance
Dunbar, Fall 2009


Course Information


.html files
.pdf files
Fall 09 Course Prospectus
prospectus09.pdf
Bibliography
Annotated Bibliography

Office Hours: 308 Avery
Monday-Wednesday-Friday: 10:30 AM - 11:20 AM.
Other times by appointment, please email me to arrange a time.


Tests, Quizzes, Projects, Homework Assignments

.html files
.pdf files
Solutions
Source files
Macros for Processing LaTeX files
macros.tex
Background Knowledge Probe
backknowprobe09.pdf
BK Probe Solutions
backknowprobe09_solns.html
backknowprobe09_solns.pdf
backknowprobe09_solns.mw
Homework 1
489f09h1.xml
489f09h1.pdf
Homework 1 Solutions
Homework 1 Solutions (.html)
Homework 1 Solutions (.pdf)
Homework 1 Solutions (Maple 13)
Homework 2
489f09h2.html
489f09h2.pdf
489f09h2.tex
Homework 2 Solutions
Homework 2 Solutions (.html)
Homework 2 Solutions (.pdf)
Homework 3
489f09h3.html
489f09h3.pdf
Homework 3 Solutions
Homework 3 Solutions (.html)
Homework 3 Solutions (.pdf)
Homework 4
489f09h4.html
489f09h4.pdf
Homework 4 Solutions
489f09h4_solns.html
489f09h4_solns.pdf
Homework 4 Solutions (Maple 13)
Homework 5
489f09h5.xml
489f09h5.pdf
Homework 5 Solutions
489f09h5_solns.html
489f09h5_solns.mw
Homework 6
489f09h6.xml
489f09h6.pdf
Homework 6 Solutions
489f09h6_solns.pdf
Sample Test 1
Fall 07 489f07t1.html
Fall 07 489f07t1.pdf
Fall 07 489f07t1_solutions.pdf
Mid-Term Test
Fall 09 489f09t1.xml
Fall 09 489f09t1.pdf
Mid-Term Solutions
Fall 09 489f09t1_solns.xml
Fall 09 489f09t1_solns.pdf
Fall 09 Test 1 Solutions in Maple
Homework 7
489f09h7.xml
489f09h7.pdf
Homework 8
489f09h8.xml
489f09h8.pdf
Homework 8 Solutions
489f09h8_solns.xml
489f09h8_solns.pdf
489f09h8_solns.mw (Maple)
Homework 9
489f09h9.xml
489f09h9.pdf

Lessons

History, Background, and Fundamentals

Brief History of Mathematical Models in Finance Theory
Updated Monday, 31-Aug-2009 05:59:56 CDT
Covered on August 25, 2003, August 22, 2005, August 27, 2007; August 24, 26, 28, 2009

Options
Updated Wednesday, 02-Sep-2009 05:37:08 CDT
Covered on August 25, 2003, August 24-26, 2005, August 29,31, 2007; August 28, 31, 2009,

Speculation and Hedging with Options
Updated Sunday, 06-Sep-2009 10:47:54 CDT
Covered on August 29, 2003, August 26,30, 2005; September 5, 2007; September 2, 2009.

Arbitrage
Updated Wednesday, 02-Sep-2009 06:12:57 CDT
Covered on September 3, 2003; August 30, 2005; September 7, 2007; September 4, 2009

Brief Remarks on Mathematical Models
Updated Sunday, 06-Sep-2009 10:49:29 CDT
Covered on September 3, 2003; September 2, 2005; September 7, 10, 2007; September 9, 2009..

Randomness
Updated Sunday, 06-Sep-2009 10:50:47 CDT
Covered on September 12, 2007; September 11, 2009.

Stochastic Processes
Updated Friday, 28-Aug-2009 06:06:49 CDT
Covered September 14, 2009.

Simple Binomial Models for Financial Derivatives

Single Period Binomial Models for Financial Derivatives
Updated Friday, 11-Sep-2009 06:09:33 CDT
Covered on September 8, 2003; September 8, 2005; Covered on September 14, 2007; September 16, 2009.

Multiple Period Binomial Models for Financial Derivatives
Updated Tuesday, 15-Sep-2009 06:09:43 CDT
Covered on September 10, 2003; September 10, 2005; September 17, 2007.

Functionals of Coin-Tossing Games, and Models of Risk

A Coin Tossing Experiment
Updated Friday, 21-Sep-2007 09:03:43 CDT
Covered on September 12, 2003; September 12, 2005; September 19, 2007; September 21, 2009.

Ruin Probabilities
Updated Sunday, 20-Sep-2009 21:37:05 CDT
Covered on September 15, 2003, September 14, 16, 19 2005; September 24, 26, 2007; September 21, 23, 25 2009

Duration of the Game till Ruin
Updated Monday, 28-Sep-2009 06:13:47 CDT Re-
Covered on September 17, 22, 2003; September 21, 2005; September 26, 28, 2007; September 28, 2009.

A Stochastic Process Model of Cash Management
Updated Sunday, 18-Oct-2009 06:45:52 CDT
Covered on September 30, October 2,5 2009.

Limit Theorems for Coin-Tossing Games

Laws of Large Numbers
Updated Wednesday, 21-Oct-2009 05:53:30 CDT
Covered on September 24,26,29, 2003; September 23, 2005; October 1, 3, 2007; October 7, 2009

Moment Generating Functions
Updated Wednesday, 07-Oct-2009 06:25:22 CDT
Covered on September 26, 2005; October 3,5, 2007; October 9, 2009.

The Central Limit Theorem
Updated Monday, 12-Oct-2009 06:01:27 CDT
Covered on September 28, 30 2005; October 10, 12, 15, 2007; October 12, 14, 2009.

The Excess of Heads over Tails, and the Arcsine Law
Updated Tuesday, 20-Oct-2009 09:55:13 CDT
Covered on September 29, October 1, 3, 2003, October 3,5, 7, 10, 2005; October 17, 19, 2007; October 16, 22, 24 2009.

Brownian Motion

Intuitive Introduction to Diffusions
Updated Monday, 26-Oct-2009 06:13:56 CDT
Covered on October 24, 2007; October 28, 2009.>

The Definition of Brownian Motion
Updated Thursday, 29-Oct-2009 06:10:20 CDT
Covered on October 8, 10, 13, 2003; October 24, 2005; October 29, 27, 2007; October 30, 2009. .

Approximation of Brownian Motion
Updated Tuesday, 03-Nov-2009 06:09:33 CST
Covered on October 15, 2003, October 26, 2005; November 2, 2007. .

Transformations of Brownian Motion
Updated Thursday, 05-Nov-2009 06:09:27 CST
Covered on October 17, 2003, October 28, 31, 2005; November 5, 2007; November 4, 2009.

Hitting Times, Gambler's Ruin, and Max Value
Updated Thursday, 05-Nov-2009 06:11:20 CST
Covered on October 22, 2003, October 31, 2005; November 7, 2007; November 6, 2009.

Path Properties
Updated Monday, 31-Oct-2005 21:37:37 CST
Covered on October 22, 2003, October 31, 2005; November 9, 2007; November 9, 2009.

Quadratic Variation of Brownian Motion
Updated Wednesday, 11-Nov-2009 06:07:06 CST
Covered on October 24,27, 2003, November 4, 2005, November 11, 2009.

Stochastic Calculus

Stochastic Differential Equations and Euler-Maruyama Method
Updated Wednesday, 09-Nov-2005 21:31:42 CST
Covered on October 31, 2003; November 9, 2005; November 13, 2009.

Ito's formula and Stochastic Calculus
Updated Wednesday, 18-Nov-2009 05:31:32 CST
Covered on November 3, 2003; November 11, 2005; November 16,18, 2009.

Geometric Brownian Motion
Updated Thursday, 19-Nov-2009 07:36:36 CST
Covered on November 5, 2003, November 14, 2005; November 20, 2009.

Black-Scholes: Derivations, Solutions, Modeling

Derivation of the Black-Scholes Equation
Updated Monday, 23-Nov-2009 06:11:46 CST
Covered on November 10,12, 2003, November 16, 18, 2005; November 23, 2009.

Solution of the Black-Scholes Equation
Updated Friday, 02-Dec-2005 20:52:25 CST
Covered on November 14, 17, 19, 24 2003; November 21, 28, 2005; .

Online Tables for Probability and Cumulative Distributions

Here are some links to Online Distribution Tables:
  1. Statsoft This site has several different distributions in a nice back-of-the-book-looking HTML format.
  2. David Lane, Rice University, Hyperstat This links to a Java applet that will compute the percentages for the normal distribution when given the Z values

Annotated Bibliography

A personal, eclectic and biased annotated bibliography of books and articles about probability, stochastic processes and mathematical finance.

Outside Readings/Links:

I check all the information on each page for correctness and typographical errors. Nevertheless, some errors may occur and I would be grateful if you would alert me to such errors. I make every reasonable effort to present current and accurate information for public use, however I do not guarantee the accuracy or timeliness of information on this website. Your use of the information from this website is strictly voluntary and at your risk.

I have checked the links to external sites for usefulness. Links to external websites are provided as a convenience. I do not endorse, control, monitor, or guarantee the information contained in any external website. I don't guarantee that the links are active at all times. Use the links here with the same caution as you would all information on the Internet. This website reflects the thoughts, interests and opinions of its author. They do not explicitly represent official positions or policies of my employer.

Information on this website is subject to change without notice.

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[ Steve Dunbar's home page ] Steve Dunbar's Home Page, http://www.math.unl.edu/~sdunbar
[ Email to Steve Dunbar ] Email to Steve Dunbar, sdunbar@unl.edu