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 2010


Course Information


.html files
.pdf files
Fall 2010 Course Prospectus
prospectus10.html
prospectus10.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

Note: In all tests, quizzes and homewrk assignments, unless specifically noted otherwise
  1. Interest is assumed to be compounded contiuously.
  2. The mathematical function log(x) means the natural logarithm, that is, logarithms to the base e.
.html files
.pdf files
Solutions
Source files
Macros for Processing LaTeX files
macros.tex
Background Knowledge Probe
backknowprobe10.pdf
backknowprobe10.tex
BK Probe Solutions
backknowprobe10_solns.html
backknowprobe10_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
489f10h2.xml
489f10h2.pdf
Homework 2 Solutions
Homework 2 Solutions (.xml)
Homework 2 Solutions (.pdf)
Homework 3
489f10h3.xml
489f10h3.pdf
Homework 3 Solutions
Homework 3 Solutions (.xml)
Homework 3 Solutions (.pdf)
Homework 4
489f10h4.xml
489f10h4.pdf
Homework 4 Solutions
489f10h4_soln.pdf
Homework 4 Solutions (Maple 13)
Homework 5
489f10h5.xml
489f10h5.pdf
Homework 5 Solutions
489f10h5_soln.xml
489f10h5_soln.pdf
Homework 6
489f10h6.xml
489f10h6.pdf
Homework 6 Solutions
489f10h6_solns.html
489f10h6_solns.pdf
489f10h6_solns.mw
Sample Test 1
Fall 09 489f09t1.xml
Fall 09 489f09t1.pdf
Fall 09 489f09t1_solns.pdf
Mid-Term Test
Fall 10 489f10t1.xml
Fall 10 489f10t1.pdf
Mid-Term Solutions
Fall 10 489f10t1_solns.xml
Fall 10 489f10t1_solns.pdf
Homework 7
489f10h7.xml
489f10h7.pdf
Homework 7 Solutions
489f10h7_solns.xml
489f10h7_solns.pdf
Homework 8
489f10h8.xml
489f10h8.pdf
Homework 8 Solutions
489f10h8_solns.xml
489f10h8_solns.pdf
Homework 9
489f10h9.xml
489f10h9.pdf
Homework 9 Solutions
489f10h9_solns.xml
489f10h9_solns.pdf
Project
Project (xml/mathml)
Project (pdf)
Project Solution
Project Solution(pdf)
Project Solution(Maple)
Homework 10
489f10h10.xml
489f10h10.pdf
Homework 10 Solutions
489f10h10_solns.pdf
489f10h10_solns.mw (Maple)
Practice Homework 11
489f10h11.xml
489f10h11.pdf
Practice Homework 11 Solutions
489f10h11_soln.pdf
489f10h11_soln.mw (Maple)
Sample Final
Fall 09 489f09f.xml
Fall 09 489f09f.pdf
Sample Final Solutions
Fall 09 489f09f_solns.pdf
Fall 09 489f09f_solns.mw (Maple)
2010 Final
Fall 10 489f10f.xml
Fall 10 489f10f.pdf
2010 Final Solutions
Fall 10 489f10f_solns.pdf
Fall 10 489f10f_solns.mw (Maple)

Lessons

Note: In all tests, quizzes and homewrk assignments, unless specifically noted otherwise

  1. Interest is assumed to be compounded contiuously.
  2. The mathematical function log(x) means the natural logarithm, that is, logarithms to the base e.

Preface

Preface (HTML, MathJax)
Updated Wednesday, 14-Sep-2016 09:57:35 CDT
Preface (PDF)
Updated Wednesday, 14-Sep-2016 09:57:32 CDT

History, Background, and Fundamentals

Brief History of Mathematical Models in Finance Theory (HTML, MathJax)
Updated Friday, 08-Jul-2016 10:57:55 CDT
Brief History of Mathematical Models in Finance Theory (PDF)
Updated Friday, 08-Jul-2016 10:57:51 CDT
Covered on August 25, 2003, August 22, 2005, August 27, 2007; August 24, 26, 28, 2009; August 23, 25, 27, 2010.

Options (HTML, MathJax)
Updated Friday, 08-Jul-2016 12:02:53 CDT
Options (PDF)
Updated Friday, 08-Jul-2016 12:02:49 CDT
Covered on August 25, 2003, August 24-26, 2005, August 29,31, 2007; August 28, 31, 2009; August 30, 2010.

Speculation and Hedging with Options (HTML, MathJax)
Updated Monday, 11-Jul-2016 11:14:52 CDT
Speculation and Hedging with Options (PDF)
Updated Monday, 11-Jul-2016 11:14:46 CDT
Covered on August 29, 2003, August 26,30, 2005; September 5, 2007; September 2, 2009; September 1, 2010.

Arbitrage (HTML, MathJax)
Updated Monday, 11-Jul-2016 11:49:17 CDT
Arbitrage (PDF)
Updated Monday, 11-Jul-2016 11:49:12 CDT
Covered on September 3, 2003; August 30, 2005; September 7, 2007; September 4, 2009; September 3, 2010.

Brief Remarks on Mathematical Models (HTML, MathJax)
Updated Thursday, 14-Jul-2016 10:45:34 CDT
Brief Remarks on Mathematical Models (PDF)
Updated Thursday, 14-Jul-2016 10:45:39 CDT
Covered on September 3, 2003; September 2, 2005; September 7, 10, 2007; September 9, 2009; September 8, 2010.

Randomness (HTML, MathJax)
Updated Friday, 15-Jul-2016 10:11:13 CDT
Randomness (PDF)
Updated Friday, 15-Jul-2016 10:11:06 CDT
Covered on September 12, 2007; September 11, 2009; September 10, 2010.

Stochastic Processes (HTML, MathJax)
Updated Friday, 15-Jul-2016 10:51:40 CDT
Stochastic Processes (PDF)
Updated Friday, 15-Jul-2016 10:47:06 CDT
Covered September 14, 2009; September 13, 2010.

A Binomial Model of CDOs (HTML, MathJax)
Updated Thursday, 08-Sep-2016 10:59:16 CDT
A Binomial Model of CDOs (PDF)
Updated Thursday, 08-Sep-2016 10:59:11 CDT
Covered September 15,17 2010.

Simple Binomial Models for Financial Derivatives

Single Period Binomial Models for Financial Derivatives (HTML, MathJax)
Updated Sunday, 17-Jul-2016 11:43:05 CDT
Single Period Binomial Models for Financial Derivatives (PDF)
Updated Sunday, 17-Jul-2016 11:43:00 CDT
Covered on September 8, 2003; September 8, 2005; Covered on September 14, 2007; September 16, 2009; September 20, 2010.

Multiple Period Binomial Models for Financial Derivatives (HTML, PDF)
Updated Sunday, 17-Jul-2016 11:41:52 CDT
Multiple Period Binomial Models for Financial Derivatives (PDF)
Updated Sunday, 17-Jul-2016 11:41:48 CDT
Covered on September 10, 2003; September 10, 2005; September 17, 2007; September 18, 2009; September 22, 2010.

General Binomial Models (HTML, MathJax)
Updated Thursday, 11-Feb-2016 09:37:46 CST
General Binomial Models (PDF)
Updated Thursday, 11-Feb-2016 09:37:48 CST

Constructing Brownian Motion and Radon-Nikodym Derivatives (PDF)
Updated Friday, 05-Feb-2016 11:07:57 CST

First Step Analysis of Coin-Tossing Games

A Coin Tossing Experiment (HTML, MathJax, GeoGebra)
Updated Monday, 18-Jul-2016 11:22:02 CDT
A Coin Tossing Experiment (PDF)
Updated Monday, 18-Jul-2016 11:21:52 CDT
Covered on September 12, 2003; September 12, 2005; September 19, 2007; September 21, 2009.

Ruin Probabilities (HTML, MathJax, GeoGebra)
Updated Monday, 18-Jul-2016 12:01:08 CDT
Ruin Probabilities (PDF)
Updated Monday, 18-Jul-2016 12:01:03 CDT
Covered on September 15, 2003, September 14, 16, 19 2005; September 24, 26, 2007; September 21, 23, 25 2009; September 24, 27, 2010.

Duration of the Game till Ruin (HTML, MathJax, GeoGebra)
Updated Monday, 12-Jun-2017 12:15:54 CDT Re-
Duration of the Game till Ruin (PDF)
Updated Monday, 12-Jun-2017 12:15:49 CDT Re-
Covered on September 17, 22, 2003; September 21, 2005; September 26, 28, 2007; September 28, 2009; September 29, 2010.

A Stochastic Process Model of Cash Management (HTML, MathJax, GeoGebra)
Updated Thursday, 21-Jul-2016 12:50:09 CDT
A Stochastic Process Model of Cash Management (PDF)
Updated Thursday, 21-Jul-2016 12:50:00 CDT
Covered on September 30, October 2,5 2009; October 4,6,2010.

Limit Theorems for Coin-Tossing Games

Laws of Large Numbers (HTML, MathJax, GeoGebra)
Updated Thursday, 21-Jul-2016 14:09:36 CDT
Laws of Large Numbers (PDF)
Updated Thursday, 21-Jul-2016 14:09:29 CDT
Covered on September 24,26,29, 2003; September 23, 2005; October 1, 3, 2007; October 7, 2009; October 8, 2010.

Moment Generating Functions (HTML, MathJax)
Updated Thursday, 21-Jul-2016 14:10:19 CDT
Moment Generating Functions (PDF)
Updated Thursday, 21-Jul-2016 14:10:13 CDT
Covered on September 26, 2005; October 3,5, 2007; October 9, 2009; October 11, 2010.

The Central Limit Theorem (HTML, MathJax, GeoGebra)
Updated Saturday, 23-Jul-2016 13:43:46 CDT
The Central Limit Theorem (PDF)
Updated Saturday, 23-Jul-2016 13:43:41 CDT
Covered on September 28, 30 2005; October 10, 12, 15, 2007; October 12, 14, 2009; October 13, 15, 2010.

The Excess of Heads over Tails (HTML, MathJax, GeoGebra)
Updated Saturday, 23-Jul-2016 13:55:48 CDT
The Excess of Heads over Tails (PDF)
Updated Saturday, 23-Jul-2016 13:55:42 CDT
Covered on September 29, October 1, 3, 2003, October 3,5, 7, 10, 2005; October 17, 19, 2007; October 16, 22, 24 2009; October 20, 22, 2010.

Brownian Motion

Intuitive Introduction to Diffusions (HTML, MathJax)
Updated Wednesday, 27-Jul-2016 13:29:12 CDT
Intuitive Introduction to Diffusions (PDF)
Updated Wednesday, 27-Jul-2016 13:29:08 CDT
Covered on October 24, 2007; October 28, 2009; October 25, 2010.

The Definition of Brownian Motion (HTML, MathJax, GeoGebra)
Updated Wednesday, 27-Jul-2016 13:53:57 CDT
The Definition of Brownian Motion (PDF)
Updated Wednesday, 27-Jul-2016 13:53:51 CDT
Covered on October 8, 10, 13, 2003; October 24, 2005; October 29, 27, 2007; October 30, 2009; October 27, 2010.

Approximation of Brownian Motion (HTML, MathJax, GeoGebra)
Updated Thursday, 28-Jul-2016 15:14:23 CDT
Approximation of Brownian Motion (PDF)
Updated Thursday, 28-Jul-2016 15:14:19 CDT
Covered on October 15, 2003, October 26, 2005; November 2, 2007; November 1, 2010.

Transformations of Brownian Motion (HTML, MathJax, GeoGebra)
Updated Thursday, 28-Jul-2016 15:26:42 CDT
Transformations of Brownian Motion (PDF)
Updated Thursday, 28-Jul-2016 15:26:37 CDT
Covered on October 17, 2003, October 28, 31, 2005; November 5, 2007; November 4, 2009; November 3, 2010.

Hitting Times and Gambler's Ruin (HTML, MathJax, GeoGebra)
Updated Monday, 01-Aug-2016 14:47:52 CDT
Hitting Times and Gambler's Ruin (PDF)
Updated Monday, 01-Aug-2016 14:47:47 CDT
Covered on October 22, 2003, October 31, 2005; November 7, 2007; November 6, 2009; November 8, 2010.

Path Properties (HTML, MathJax, GeoGebra)
Updated Monday, 01-Aug-2016 15:04:38 CDT
Path Properties (PDF)
Updated Monday, 01-Aug-2016 15:04:32 CDT
Covered on October 22, 2003, October 31, 2005; November 9, 2007; November 9, 2009; November 10, 2010.

Quadratic Variation of Brownian Motion (HTML, MathJax)
Updated Tuesday, 02-Aug-2016 11:22:24 CDT
Quadratic Variation of Brownian Motion (PDF)
Updated Tuesday, 02-Aug-2016 11:22:19 CDT
Covered on October 24,27, 2003, November 4, 2005, November 11, 2009; November 15,2010.

Stochastic Calculus

Stochastic Differential Equations and Euler-Maruyama Method (HTML, MathJax)
Updated Tuesday, 02-Aug-2016 11:36:11 CDT
Stochastic Differential Equations and Euler-Maruyama Method (PDF)
Updated Tuesday, 02-Aug-2016 11:36:02 CDT
Covered on October 31, 2003; November 9, 2005; November 13, 2009; November 17, 2010.

Ito's formula and Stochastic Calculus (HTML, MathJax)
Updated Thursday, 04-Aug-2016 15:26:29 CDT
Ito's formula and Stochastic Calculus (PDF)
Updated Thursday, 04-Aug-2016 15:26:26 CDT
Covered on November 3, 2003; November 11, 2005; November 16,18, 2009; November 19, 2010.

Geometric Brownian Motion (HTML, MathJax)
Updated Thursday, 04-Aug-2016 15:25:23 CDT
Geometric Brownian Motion (PDF)
Updated Thursday, 04-Aug-2016 15:25:14 CDT
Covered on November 5, 2003, November 14, 2005; November 20, 2009, November 22, 2010.

Models of Stock Market Prices (HTML, MathJax)
Updated Monday, 08-Aug-2016 08:27:05 CDT
Models of Stock Market Prices (PDF)
Updated Monday, 08-Aug-2016 08:27:00 CDT

Monte Carlo Simulation of Option Prices (HTML, MathJax)
Updated Monday, 08-Aug-2016 08:40:03 CDT
Monte Carlo Simulation of Options Prices (PDF)
Updated Monday, 08-Aug-2016 08:39:56 CDT

Presentation on Importance Sampling in Monte Carlo Simulation of Option Prices (PDF)
Updated Monday, 25-Jan-2016 09:06:52 CST

Presentation on Importance Sampling and Radon-Nikodym Derivatives (PDF)
Updated Tuesday, 02-Feb-2016 07:24:53 CST

Black-Scholes: Derivations, Solutions, Modeling

Derivation of the Black-Scholes Equation (HTML, Mathjax)
Updated Wednesday, 24-Aug-2016 13:22:08 CDT
Derivation of the Black-Scholes Equation (PDF)
Updated Wednesday, 24-Aug-2016 13:22:04 CDT
Covered on November 10,12, 2003, November 16, 18, 2005; November 23, 30, 2009; November 29, December 1, 2010.

Solution of the Black-Scholes Equation (HTML, MathJax, Geogebra)
Updated Wednesday, 24-Aug-2016 13:22:55 CDT
Solution of the Black-Scholes Equation (PDF)
Updated Wednesday, 24-Aug-2016 13:22:47 CDT
Covered on November 14, 17, 19, 24 2003; November 21, 28, 2005; December 2,4 2009; December 3,6, 2010.

Put-Call Parity Principle (HTML, MathJax, Geogebra)
Updated Wednesday, 24-Aug-2016 13:24:55 CDT
Put-Call Parity Principle (PDF)
Updated Wednesday, 24-Aug-2016 13:24:49 CDT
Covered on December 1, 2003, November 30, December 2, 2005; December 7, 2009; December 8, 2010.

Implied Volatility (HTML, MathJax, Geogebra)
Updated Wednesday, 24-Aug-2016 13:25:41 CDT
Implied Volatility (PDF)
Updated Wednesday, 24-Aug-2016 13:25:36 CDT
Covered on December 1, 2003; December 7, 2009.

Sensitivity, Hedging, and the "Greeks" (HTML, MathJax, Geogebra)
Updated Wednesday, 24-Aug-2016 13:26:41 CDT
Sensitivity, Hedging, and the "Greeks" (PDF)
Updated Wednesday, 24-Aug-2016 13:26:35 CDT
Covered on December 8,10, 2003; December 2, 2005.

Limitations of the Black-Scholes model (HTML, MathJax)
Updated Wednesday, 07-Sep-2016 14:33:22 CDT
Limitations of the Black-Scholes model (PDF)
Updated Wednesday, 07-Sep-2016 14:33:16 CDT
Covered on December 12, 2003; December 5, 2005, December 11, 2009; December 10, 2010.

Testing Financial Data for Fat Tails (HTML, MathJax)
Updated Wednesday, 24-Aug-2016 13:28:42 CDT
Testing Financial Data for Fat Tails (PDF)
Updated Wednesday, 24-Aug-2016 13:28:38 CDT

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.
  3. StatTrek Statistical Tables Binomial Calculator An easy-to-use applet that calculates binomial probabilities along with cumulative distribution functions and complementary cumulative distribution functions. Tabs/links at the top of the page connect to similar calculators for the chi-square, f-distribution, hypergeometric, multinomial, negative binomial, normal, Poisson, and t-distribution PDF and CDFs as well. Finally on each page, there are short descriptions and explanations in the form of Frequently Asked Questions.

Annotated Bibliography

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

Outside Readings/Links:

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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