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

[an error occurred while processing this directive]

# Course Information

EDU (Web Quizzes) Page for Stochastic Processes and Advanced mathematical Finance EDU: 489/889 Fall07 Dunbar

 .html files .pdf files Fall 07 Course Prospectus prospectus07.html prospectus07.pdf Fall 07 Tests and Grading Fall 07 Course Grades Link Policy Links/Bookmarks Course bookmarks on del.icio.us Bibliography Annotated Bibligraphy

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 .tex files Macros for Processing LaTeX files macros.tex Background Knowledge Probe backknowprobe07.html backknowprobe07.pdf backknowprobe07.tex Background Knowledge Solutions backknowprobe07_solns.html backknowprobe07_solns.mw Homework 1 489f07h1.html 489f07h1.pdf 489f07h1.tex Homework 1 Solutions 489f07h1_soln.html 489f07h1_soln.mw Homework 2 489f07h2.html 489f07h2.pdf 489f07h2.tex Homework 2 Solutions 489f07h2_solns.html 489f07h2_solns.pdf 489f07h2_solns.tex Homework 3 489f07h3.html 489f07h3.pdf 489f07h3.tex Homework 3 Solutions 489f07h3_solns.html 489f07h3_solns.pdf 489f07h3_solns.tex Homework 4 489f07h4.html 489f07h4.pdf 489f07h4_stripped.tex Homework 4 Solutions 489f07h4_solns.html 489f07h4_solns.pdf 489f07h4_solns.tex Homework 5 489f07h5.html 489f07h5.pdf 489f07h5_stripped.tex Homework 5 Solutions 489f07h5_solns.html 489f07h5_solns.pdf 489f07h5_solns.tex Sample Test 1 Fall 05 489f05t1.html Fall 05 489f05t1.pdf Fall 05 489f05t1_soln.pdf Mid-Term Test Fall 07 489f07t1.html Fall 07 489f07t1.pdf Mid-Term Solutions Fall 07 489f07t1_solutions.html Fall 07 489f07t1_solutions.pdf Homework 6 489f07h6.html 489f07h6.pdf 489f07h6_stripped.tex Homework 6 Solutions 489f07h6_solutions.html 489f07h6_solutions.pdf 489f07h6_solns.mw (Maple) Homework 7 489f07h7.html 489f07h7.pdf 489f07h7_stripped.tex Homework 7 Solutions 489f07h7_solutions.html 489f07h7_solutions.pdf Homework 8 489f07h8.html 489f07h8.pdf 489f07h8_stripped.tex Homework 8 Solutions 489f07h8_solutions.html 489f07h8_solutions.pdf 489f07h8_solns.mw (Maple) Homework 9 489f07h9.html 489f07h9.pdf 489f07h9_stripped.tex Homework 9 Solutions 489f07h9_solutions.html 489f07h9_solutions.pdf 489f07h9_solns.mw (Maple) Homework 10 489f07h10.html 489f07h10.pdf 489f07h10_stripped.tex Homework 10 Solutions 489f07h10_solutions.html 489f07h10_solutions.pdf Sample Final Fall 05 489f05f.html Fall 05 489f05f.pdf Sample Final Solutions Fall 05 489f05f_solutions.html Fall 05 489f05f_solutions.pdf

# Lessons

## History, Background, and Fundamentals

Brief History of Mathematical Models in Finance Theory
Updated [an error occurred while processing this directive]
Covered on August 25, 2003, August 22, 2005, August 27, 2007

Options
Updated [an error occurred while processing this directive], Re-Frozen
Covered on August 25, 2003, August 24-26, 2005, August 29,31, 2007

Speculation and Hedging with Options
Updated [an error occurred while processing this directive], Frozen
Covered on August 29, 2003, August 26,30, 2005; September 5, 2007

Arbitrage
Updated [an error occurred while processing this directive] Frozen
Covered on September 3, 2003; August 30, 2005; September 7, 2007

Brief Remarks on Mathematical Models
Updated [an error occurred while processing this directive] Frozen
Covered on September 3, 2003; September 2, 2005; September 7, 10, 2007.

Randomness
Updated [an error occurred while processing this directive] Frozen
Covered on September 12, 2007.

## Simple Binomial Models for Financial Derivatives

Simple Binomial Models for Financial Derivatives
Updated [an error occurred while processing this directive] Frozen
Covered on September 8, 2003; September 8, 2005; Covered on September 14, 2007.

Binomial Tree Models for Financial Derivatives
Updated [an error occurred while processing this directive] Frozen
Covered on September 10, 2003; September 10, 2005; September 17, 2007.

## Coin-Tossing Games, the Gambler's Ruin and Volatility

A Coin Tossing Experiment
Updated [an error occurred while processing this directive] Frozen
Covered on September 12, 2003; September 12, 2005; September 19, 2007.

Ruin Probabilities
Updated [an error occurred while processing this directive] Frozen
Covered on September 15, 2003, September 14, 16, 19 2005; September 24, 26, 2007

Duration of the Game till Ruin
Updated [an error occurred while processing this directive] Re-Frozen
Covered on September 17, 22, 2003; September 21, 2005; September 26, 28, 2007.

Laws of Large Numbers
Updated [an error occurred while processing this directive]
Covered on September 24,26,29, 2003; September 23, 2005; October 1, 3, 2007. Frozen

Moment Generating Functions
Updated [an error occurred while processing this directive]
Covered on September 26, 2005; October 3,5, 2007. Frozen.

The Central Limit Theorem
Updated [an error occurred while processing this directive]
Covered on September 28, 30 2005; October 10, 12, 15, 2007. Re-Frozen

The Excess of Heads over Tails, and the Arcsine Law
Updated [an error occurred while processing this directive] Frozen
Covered on September 29, October 1, 3, 2003, October 3,5, 7, 10, 2005; October 17, 19, 2007.

The Law of the Iterated Logarithm
Updated [an error occurred while processing this directive]
Covered on October 6, 2003, October 12, 19, 2005. Frozen.

Intuitive Introduction to Diffusions Covered on October 24, 2007.

## Brownian Motion

The Definition of Brownian Motion
Updated [an error occurred while processing this directive]
Covered on October 8, 10, 13, 2003; October 24, 2005; October 29, 27, 2007. Frozen.

Approximation of Brownian Motion
Updated [an error occurred while processing this directive]
Covered on October 15, 2003, October 26, 2005; November 2, 2007. Frozen.

Transformations of Brownian Motion
Updated [an error occurred while processing this directive]
Covered on October 17, 2003, October 28, 31, 2005; November 5, 2007. Frozen.

Hitting Times, Gambler's Ruin, and Max Value
Updated [an error occurred while processing this directive]
Covered on October 22, 2003, October 31, 2005; November 7, 2007. Frozen.

Path Properties
Updated [an error occurred while processing this directive]
Covered on October 22, 2003, October 31, 2005; November 9, 2007; Frozen.

Quadratic Variation of Brownian Motion
Updated [an error occurred while processing this directive]
Covered on October 24,27, 2003, November 4, 2005. Frozen.

## Stochastic Calculus

Ordinary Differential Equations and Euler's Method
Updated [an error occurred while processing this directive]
Covered on October 29, 2003.

Stochastic Differential Equations and Euler-Maruyama Method
Updated [an error occurred while processing this directive]
Covered on October 31, 2003, November 9, 2005. Frozen.

Ito's formula and Stochastic Calculus
Updated [an error occurred while processing this directive]
Covered on November 3, 2003; November 11, 2005. Frozen.

Geometric Brownian Motion
Updated [an error occurred while processing this directive]
Covered on November 5, 2003, November 14, 2005. Frozen

## Black-Scholes: Derivations, Solutions, Examples

Derivation of the Black-Scholes Equation
Updated [an error occurred while processing this directive]
Covered on November 10,12, 2003, November 16, 18, 2005. Frozen.

Solution of the Black-Scholes Equation
Updated [an error occurred while processing this directive]
Covered on November 14, 17, 19, 24 2003; November 21, 28, 2005. Re-Frozen.

Put-Call Parity Principle
Updated [an error occurred while processing this directive]
Covered on December 1, 2003, November 30, December 2, 2005. Frozen.

Implied Volatility
Updated [an error occurred while processing this directive]
Covered on December 1, 2003.

Sensitivity, Hedging, and the "Greeks"
Updated [an error occurred while processing this directive]
Covered on December 8,10, 2003; December 2, 2005. Frozen.

Limitations of the Black-Scholes model
Updated [an error occurred while processing this directive]
Covered on December 12, 2003; December 5, 2005. Frozen

## Counting and Poisson Processes

Introduction to Counting and Poisson Processes
Updated [an error occurred while processing this directive]
Covered on January 12, 14, 16, 2004.

The Poisson Approximation to the Binomial
Updated [an error occurred while processing this directive]
Covered on January 21, 2004.

## Conditional Probability and Expectation

Conditional Probability
Updated [an error occurred while processing this directive]
Covered on January 26, February 2, 2004.

Conditional Expectations
Updated [an error occurred while processing this directive]
Covered on February 2, 4,6 2004.

Random Sums
Updated [an error occurred while processing this directive]
Covered on February 9, 11, 2004.

## Martingales

Definition of Martingales and Basic Properties
Updated [an error occurred while processing this directive]
Covered on February 16, 18, 2004.

Stopping Times and the Optional Stopping Theorem
Updated [an error occurred while processing this directive]
Covered on February 18, 20, 2004.

Bounds on American Options
Updated [an error occurred while processing this directive]
Covered on February 23, 2004.

American Options
Updated [an error occurred while processing this directive]
Covered on March 3, 2004.

## American Put Options and Free Boundary Problems

Boundary Conditions
Updated [an error occurred while processing this directive]
Covered on April 12, 14 2004.

Putting the American Put Problem in Linear Complementarity Form
Updated [an error occurred while processing this directive]
Covered on April 16, 2004.

## Markov Process Variants

Review of Markov Chains
Updated [an error occurred while processing this directive]

Review of Matrices
Updated [an error occurred while processing this directive]

Hidden Markov Models
Updated [an error occurred while processing this directive]
Covered in seminar, January 28, 2005.

Hidden Markov Models
Updated [an error occurred while processing this directive]
Covered in seminar, January 28, 2005.

Rumors Model Maple 10 Worksheet with maplets

Updated [an error occurred while processing this directive]

## 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.

A personal, eclectic and biased bibliography of books I have noted or consulted while preparing the materials for the course.

## Anonymous Feedback Form

Anonymous Feedback Page allowing students to email some anonymous comments, questions, criticisms, suggestions, or corrections or anything else about the course. All mail goes directly to me, but without names!