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.

## 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; August 24, 26, 28, 2009; August 23, 25, 27, 2010.

Options
Updated [an error occurred while processing this directive]
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
Updated [an error occurred while processing this directive]
Covered on August 29, 2003, August 26,30, 2005; September 5, 2007; September 2, 2009; September 1, 2010.

Arbitrage
Updated [an error occurred while processing this directive]
Covered on September 3, 2003; August 30, 2005; September 7, 2007; September 4, 2009; September 3, 2010.

Brief Remarks on Mathematical Models
Updated [an error occurred while processing this directive]
Covered on September 3, 2003; September 2, 2005; September 7, 10, 2007; September 9, 2009; September 8, 2010.

Randomness
Updated [an error occurred while processing this directive]
Covered on September 12, 2007; September 11, 2009; September 10, 2010.

Stochastic Processes
Updated Wednesday, 15-Sep-2010 05:48:56 CDT
Covered September 14, 2009; September 13, 2010.

A Binomial Model of CDOs
Updated [an error occurred while processing this directive]
Covered September 15,17 2010.

## Simple Binomial Models for Financial Derivatives

Single Period Binomial Models for Financial Derivatives
Updated [an error occurred while processing this directive]
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
Updated Wednesday, 23-Dec-2015 09:59:16 CST
Covered on September 10, 2003; September 10, 2005; September 17, 2007; September 18, 2009; September 22, 2010.

## First Step Analysis of Coin-Tossing Games

A Coin Tossing Experiment
Updated [an error occurred while processing this directive]
Covered on September 12, 2003; September 12, 2005; September 19, 2007; September 21, 2009.

Ruin Probabilities
Updated Monday, 08-Apr-2013 05:46:38 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
Updated Friday, 05-Apr-2013 05:41:56 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
Updated [an error occurred while processing this directive]
Covered on September 30, October 2,5 2009; October 4,6,2010.

## Limit Theorems for Coin-Tossing Games

Laws of Large Numbers
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
Updated Thursday, 28-Feb-2013 05:44:02 CST
Covered on September 26, 2005; October 3,5, 2007; October 9, 2009; October 11, 2010.

The Central Limit Theorem
Updated [an error occurred while processing this directive]
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
Updated [an error occurred while processing this directive]
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
Updated [an error occurred while processing this directive]
Covered on October 24, 2007; October 28, 2009; October 25, 2010.

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; October 30, 2009; October 27, 2010.

Approximation of Brownian Motion
Updated [an error occurred while processing this directive]
Covered on October 15, 2003, October 26, 2005; November 2, 2007; November 1, 2010.

Transformations of Brownian Motion
Updated [an error occurred while processing this directive]
Covered on October 17, 2003, October 28, 31, 2005; November 5, 2007; November 4, 2009; November 3, 2010.

Hitting Times and Gambler's Ruin
Updated [an error occurred while processing this directive]
Covered on October 22, 2003, October 31, 2005; November 7, 2007; November 6, 2009; November 8, 2010.

Path Properties
Updated [an error occurred while processing this directive]
Covered on October 22, 2003, October 31, 2005; November 9, 2007; November 9, 2009; November 10, 2010.

Updated [an error occurred while processing this directive]
Covered on October 24,27, 2003, November 4, 2005, November 11, 2009; November 15,2010.

## Stochastic Calculus

Stochastic Differential Equations and Euler-Maruyama Method
Updated [an error occurred while processing this directive]
Covered on October 31, 2003; November 9, 2005; November 13, 2009; November 17, 2010.

Ito's formula and Stochastic Calculus
Updated [an error occurred while processing this directive]
Covered on November 3, 2003; November 11, 2005; November 16,18, 2009; November 19, 2010.

Geometric Brownian Motion
Updated [an error occurred while processing this directive]
Covered on November 5, 2003, November 14, 2005; November 20, 2009, November 22, 2010.

## Black-Scholes: Derivations, Solutions, Modeling

Derivation of the Black-Scholes Equation
Updated [an error occurred while processing this directive]
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
Updated [an error occurred while processing this directive]
Covered on November 14, 17, 19, 24 2003; November 21, 28, 2005; December 2,4 2009; December 3,6, 2010.

Put-Call Parity Principle
Updated Saturday, 04-Dec-2010 07:20:04 CST
Covered on December 1, 2003, November 30, December 2, 2005; December 7, 2009; December 8, 2010.

Implied Volatility
Updated [an error occurred while processing this directive]
Covered on December 1, 2003; December 7, 2009.

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

Limitations of the Black-Scholes model
Updated [an error occurred while processing this directive]
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.