Advanced Financial Mathematics
Math 324
Spring 2007
Classes:W: 2:05 – 2:50 MSB307 Instructor: James G. Bridgeman, FSA
F: 1:00 – 2:45 TLS 301 MSB408
Office Hours: M 10:00 – 11:00,1:002:00 8604868382
Th 10:00 –12:00,2:003:00 bridgeman@math.uconn.edu
F 10:00 –11:00 websites: instructor’s math.uconn.edu/~bridgeman
Or by
appointment course: math.uconn.edu/~bridgeman/math324s07/index.html
Context for the Course
Required for the
Professional Master’s degree in Applied Financial Mathematics; contains
material relevant for SOA exams MFE and C
The Standard Models for Pricing and Replicating Financial Instruments (such as Derivatives) Presented Within the Context of the Theory of Continuous Stochastic Processes and Stochastic Calculus
Steven Shreve, Stochastic Calculus for Finance II
Note errata posted at www.math.cmu.edu/users/shreve/ErrataVolIISep06.pdf; and www.math.cmu.edu/users/shreve/ErrataVolIINov06.pdf
Richard Bass, The Basics of Financial Mathematics (highly
recommended)
www.math.uconn.edu/~bass/finlmath.pdf
Alison Etheridge, A Course in Financial Calculus
Steven Shreve, Stochastic Calculus for Finance I
Ho & Lee, The
R. McDonald, Derivatives Markets (2^{nd} Ed.)
Takehome Tests 30%
Paper/Project 35%
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) 
Text Sections 

Jan. 15 
Review of Probability 
ch. 1 

Jan. 22 
Conditioning 
ch. 2 

Jan. 29 
Random Walk and Brownian Motion 
Sec. 3.13.5 

Feb. 5 
Brownian Motion; Stochastic Calculus: Itô Integral 
Sec. 3.63.8, 4.14.3 

Feb. 12 
Itô’s Lemma; Black–Scholes Equation 
Sec.4.44.5.3 

Feb. 19 
Solution and Properties of Black–Scholes Equation; Multivariate Stochastic Calculus 
Sec. 4.5.44.6, 4.8 

Feb. 26 
RiskNeutral Measure: Girsanov’s Theorem, Martingale Representation Theorem, Hedging 
Sec. 5.15.3 

March 12 
Fundamental Theorem of Asset Pricing: existence and uniqueness of Risk Neutral Measure 
Sec. 5.4 

March 19 
Basic Applications to Financial Assets 
Sec. 5.55.7 

March 26 
Connection With Partial Differential Equations 
Sec. 6.16.5 

April 2 
Further Topics For Applying the Model 
TBD from Ch. 710 

April 9 
Further Topics For Applying the Model 
TBD 

April 16 
Further Topics For Applying the Model 
TBD 

April 23 
Further Topics For Applying the Model 
TBD 


Final Exam TBD week of Apr 30 to May 5 
All 

To master the material and be prepared for the final exam you should expect to do most of the exercises in the textbook as part of your studying each chapter. Specific exercises will be assigned and they are fair game for the final exam. These will not be collected and graded so it’s up to you to ask questions about the ones you don’t feel comfortable with.
Take Home Tests
There will be two or three take home tests given and graded over the course of the semester, at about the level of difficulty of the text exercises and sometimes drawn directly from the text exercises.
You will be expected to produce a term paper or a modeling project, due by April 30. This can be a topic that you select from the parts of the text that we don’t cover or one that goes beyond the level at which we do cover something. If you can’t come up with a topic that interests you, one will be assigned.
Both the syllabus and the grading plan are subject to change with appropriate advance notice to the class.