Department of
Mathematics 203 Avery Hall University of Nebraska Lincoln Lincoln, NE 685880323 4024723731 (voice) 4024728466 (fax) 








Office Hours: 308 Avery
MondayWednesdayFriday: 10:30 AM  11:20 AM.
Other times by appointment, please email me to arrange a time.
Note: In all tests, quizzes and homewrk assignments, unless specifically noted otherwise
Preface
(HTML, MathJax)
Updated Wednesday, 14Sep2016 09:57:35 CDT
Preface
(PDF)
Updated Wednesday, 14Sep2016 09:57:32 CDT
Brief History of Mathematical Models in Finance Theory
(HTML, MathJax)
Updated Friday, 08Jul2016 10:57:55 CDT
Brief History of Mathematical Models in Finance Theory
(PDF)
Updated Friday, 08Jul2016 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, 08Jul2016 12:02:53 CDT
Options (PDF)
Updated Friday, 08Jul2016 12:02:49 CDT
Covered on August 25, 2003, August 2426, 2005, August 29,31,
2007; August 28, 31, 2009; August 30, 2010.
Speculation and Hedging with Options (HTML, MathJax)
Updated Monday, 11Jul2016 11:14:52 CDT
Speculation and Hedging with Options (PDF)
Updated Monday, 11Jul2016 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, 11Jul2016 11:49:17 CDT
Arbitrage (PDF)
Updated Monday, 11Jul2016 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, 14Jul2016 10:45:34 CDT
Brief Remarks on Mathematical Models (PDF)
Updated Thursday, 14Jul2016 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, 15Jul2016 10:11:13 CDT
Randomness (PDF)
Updated Friday, 15Jul2016 10:11:06 CDT
Covered on September 12, 2007; September 11, 2009; September
10, 2010.
Stochastic Processes (HTML, MathJax)
Updated Friday, 15Jul2016 10:51:40 CDT
Stochastic Processes (PDF)
Updated Friday, 15Jul2016 10:47:06 CDT
Covered September 14, 2009; September 13, 2010.
A Binomial Model of CDOs (HTML, MathJax)
Updated Thursday, 08Sep2016 10:59:16 CDT
A Binomial Model of CDOs (PDF)
Updated Thursday, 08Sep2016 10:59:11 CDT
Covered September 15,17 2010.
Single Period Binomial Models for Financial Derivatives (HTML, MathJax)
Updated Sunday, 17Jul2016 11:43:05 CDT
Single Period Binomial Models for Financial Derivatives
(PDF)
Updated Sunday, 17Jul2016 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, 17Jul2016 11:41:52 CDT
Multiple Period Binomial Models for Financial Derivatives
(PDF)
Updated Sunday, 17Jul2016 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, 11Feb2016 09:37:46 CST
General Binomial Models
(PDF)
Updated Thursday, 11Feb2016 09:37:48 CST
Constructing Brownian Motion and RadonNikodym Derivatives
(PDF)
Updated Friday, 05Feb2016 11:07:57 CST
A Coin Tossing Experiment (HTML, MathJax, GeoGebra)
Updated Monday, 18Jul2016 11:22:02 CDT
A Coin Tossing Experiment (PDF)
Updated Monday, 18Jul2016 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, 18Jul2016 12:01:08 CDT
Ruin Probabilities (PDF)
Updated Monday, 18Jul2016 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, 12Jun2017 12:15:54 CDT Re
Duration of the Game till Ruin (PDF)
Updated Monday, 12Jun2017 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, 21Jul2016 12:50:09 CDT
A Stochastic Process Model of Cash Management (PDF)
Updated Thursday, 21Jul2016 12:50:00 CDT
Covered on September 30, October 2,5 2009; October 4,6,2010.
Laws of Large Numbers (HTML, MathJax, GeoGebra)
Updated Thursday, 21Jul2016 14:09:36 CDT
Laws of Large Numbers (PDF)
Updated Thursday, 21Jul2016 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, 21Jul2016 14:10:19 CDT
Moment Generating Functions (PDF)
Updated Thursday, 21Jul2016 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, 23Jul2016 13:43:46 CDT
The Central Limit Theorem (PDF)
Updated Saturday, 23Jul2016 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, 23Jul2016 13:55:48 CDT
The Excess of Heads over Tails (PDF)
Updated Saturday, 23Jul2016 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.
Intuitive Introduction to Diffusions (HTML, MathJax)
Updated Wednesday, 27Jul2016 13:29:12 CDT
Intuitive Introduction to Diffusions (PDF)
Updated Wednesday, 27Jul2016 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, 27Jul2016 13:53:57 CDT
The Definition of Brownian Motion (PDF)
Updated Wednesday, 27Jul2016 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, 28Jul2016 15:14:23 CDT
Approximation of Brownian Motion (PDF)
Updated Thursday, 28Jul2016 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, 28Jul2016 15:26:42 CDT
Transformations of Brownian Motion (PDF)
Updated Thursday, 28Jul2016 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, 01Aug2016 14:47:52 CDT
Hitting Times and Gambler's Ruin (PDF)
Updated Monday, 01Aug2016 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, 01Aug2016 15:04:38 CDT
Path Properties (PDF)
Updated Monday, 01Aug2016 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 Monday, 18May2020 09:49:31 CDT
Quadratic Variation of Brownian Motion (PDF)
Updated Monday, 18May2020 09:49:24 CDT
Covered on October 24,27, 2003, November 4, 2005, November 11,
2009; November 15,2010.
Stochastic Differential Equations and EulerMaruyama
Method (HTML, MathJax)
Updated Tuesday, 02Aug2016 11:36:11 CDT
Stochastic Differential Equations and EulerMaruyama
Method (PDF)
Updated Tuesday, 02Aug2016 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, 04Aug2016 15:26:29 CDT
Ito's formula and Stochastic Calculus (PDF)
Updated Thursday, 04Aug2016 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, 04Aug2016 15:25:23 CDT
Geometric Brownian Motion (PDF)
Updated Thursday, 04Aug2016 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, 08Aug2016 08:27:05 CDT
Models of Stock Market Prices (PDF)
Updated Monday, 08Aug2016 08:27:00 CDT
Monte Carlo Simulation of Option Prices (HTML, MathJax)
Updated Monday, 08Aug2016 08:40:03 CDT
Monte Carlo Simulation of Options Prices (PDF)
Updated Monday, 08Aug2016 08:39:56 CDT
Presentation on Importance Sampling in Monte Carlo
Simulation of Option Prices (PDF)
Updated Monday, 25Jan2016 09:06:52 CST
Presentation on Importance Sampling and RadonNikodym Derivatives (PDF)
Updated Tuesday, 02Feb2016 07:24:53 CST
Derivation of the BlackScholes Equation (HTML, Mathjax)
Updated Wednesday, 24Aug2016 13:22:08 CDT
Derivation of the BlackScholes Equation (PDF)
Updated Wednesday, 24Aug2016 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 BlackScholes Equation (HTML, MathJax, Geogebra)
Updated Wednesday, 24Aug2016 13:22:55 CDT
Solution of the BlackScholes Equation (PDF)
Updated Wednesday, 24Aug2016 13:22:47 CDT
Covered on November 14, 17, 19, 24 2003; November 21, 28,
2005; December 2,4 2009; December 3,6, 2010.
PutCall Parity Principle (HTML, MathJax, Geogebra)
Updated Wednesday, 24Aug2016 13:24:55 CDT
PutCall Parity Principle (PDF)
Updated Wednesday, 24Aug2016 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, 24Aug2016 13:25:41 CDT
Implied Volatility (PDF)
Updated Wednesday, 24Aug2016 13:25:36 CDT
Covered on December 1, 2003; December 7, 2009.
Sensitivity, Hedging, and the "Greeks" (HTML, MathJax, Geogebra)
Updated Wednesday, 24Aug2016 13:26:41 CDT
Sensitivity, Hedging, and the "Greeks" (PDF)
Updated Wednesday, 24Aug2016 13:26:35 CDT
Covered on December 8,10, 2003; December 2, 2005.
Limitations of the BlackScholes model (HTML, MathJax)
Updated Wednesday, 07Sep2016 14:33:22 CDT
Limitations of the BlackScholes model (PDF)
Updated Wednesday, 07Sep2016 14:33:16 CDT
Covered on December 12, 2003; December 5, 2005, December 11,
2009; December 10, 2010.
A personal, eclectic and biased annotated bibliography of books and articles about probability, stochastic processes and mathematical finance.
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Steve Dunbar's Home Page, http://www.math.unl.edu/~sdunbar