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)

[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.

Applications of Geometric Brownian Motion to Warrants

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

Self-financing portfolios with examples

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]

Jumps and Shocks in Financial Applications

The Stochastic Differential Equation for a Jump-Diffusion Process

A Poisson Jump Volatility Model for Option Prices

A Black-Scholes type equation for options on securities following a jump-diffusion

Interest Rate Models

Interest Rate Markets: Basic Definitions

A Simple Single Factor Model

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!

Outside Readings/Links:

[an error occurred while processing this directive]

[an error occurred while processing this directive]

[ 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