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

# 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.

## 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.