Advanced Financial Mathematics
Math 324
Spring 2006
Classes: MWF: 1:00 – 1:50 Instructor: James G. Bridgeman, FSA
MSB411 MSB408
Office Hours: M 10:00 – 12:00 8604868382
Th 10:00 –12:00 bridgeman@math.uconn.edu
Th/F: 2:00
 3:00 websites: instructor’s math.uconn.edu/~bridgeman
Or by appointment course: math.uconn.edu/~bridgeman/math324s06/index.html
Context for the Course
Required for the
Professional Master’s degree in Applied Financial Mathematics
The Standard Models for Pricing and Replicating Financial Instruments (such as Derivatives) Presented Within the Context of the Theory of Stochastic Processes and Stochastic Calculus
Alison Etheridge, A Course in Financial Calculus
Bass, The Basics of Financial
Mathematics www.math.uconn.edu/~bass/finlmath.pdf
Ho & Lee, The
Graded Homework 40%
Paper/Project 25%
Final Exam 35%
Both the syllabus and the grading plan are subject to change with appropriate advance notice to the class.
Outline & Intended Pace



Week of 
Topic(s) 
Sections 

Jan. 16 
Simple options and forwards; toy models; noarbitrage principle 
1.11.5 

Jan. 23 
Riskneutral probabilities; binary trees; discrete stochastic processes 
1.62.3 

Jan. 30 
Conditional expectations; martingales; markov processes; discrete stochastic integrals; equivalent martingale measure; properties of martingales 
2.32.4, notes 

Feb. 6 
Compensation; binomial representation theorem; continuous limit; definition of Brownian motion 
2.43.1, notes 

Feb. 13 
Construction and properties of Brownian motion; continuous martingales 
3.23.4, notes 

Feb. 20 
Properties of martingales; arbitrage and variation; stochastic integration 
3.44.2, notes 

Feb. 27 
Stochastic integration; Itô’s calculus 
4.24.3, notes 

March 13 
Stochastic differential equations; more stochastic calculus; Girsanov’s Thm. 
4.34.5, notes 

March 20 
Brownian martingale representation; FeynmanKac representation; selffinancing; equivalent martingale measure; Fund. Thm. of Asset Pricing 
4.65.1, notes 

March 27 
BlackScholes; replicating portfolios; foreign exchange; dividends 
5.25.4 

April 3 
Bonds; market price of risk; interest rate models 
5.55.6, notes 

April 10 
Exotics; American options 
6.16.5 

April 17 
Generalized BlackScholes; multiple assets; multivariate stochastic calculus 
7.17.2 

April 24 
Quantos; jump models; hedging error; stochastic volatility 
7.27.4 


Final Exam TBD week of May 1  6 
All 

To master the material and be prepared for the final exam you should expect to do essentially all of the exercises in the textbook. There will be six specific assignments collected and graded, drawn mostly from the text exercises but supplemented with other questions.
You will be expected to produce a term paper or a modeling project, due by April 26. Details of what’s expected will be provided by a couple of weeks into the course
Both the syllabus and the grading plan are subject to change with appropriate advance notice to the class.