Advanced Financial Mathematics
Math 324
Spring 2008
Classes:W: 2:00 – 2:50 MSB411 Instructor: James G. Bridgeman, FSA
F: 1:00 – 2:50 BRON124 MSB408
Office Hours: M/Th 10:00 – 11:00 8604868382
W 11:00 –12:00 bridgeman@math.uconn.edu
Th 2:00 – 3:00 websites:
instructor’s: www.math.uconn.edu/~bridgeman/index.htm
Or by appointment course: www.math.uconn.edu/~bridgeman/math324s08/index.htm
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 Continuous Time Models, Springer 2004
Note errata posted at www.math.cmu.edu/users/shreve/ErrataVolIISep06.pdf; and More errata for 2004 printing of Volume II, July 2007
Richard Bass, The Basics of Financial Mathematics (highly
recommended)
www.math.uconn.edu/~bass/finlmath.pdf
Alison Etheridge, A Course in Financial Calculus, Cambridge 2002
Steven Shreve, Stochastic Calculus for Finance I The Binomial Asset Pricing Model, Springer 2004
Ho & Lee, The Oxford Guide to Financial Modeling, Oxford 2004
R. McDonald, Derivatives Markets (2^{nd} Ed.), Pearson
AddisonWesley 2006
Brigo & Mercurio, Interest Rate
ModelsTheory and Practice (2^{nd} Ed.,3^{rd}
printing), Springer 2007
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. 21 
Main Ideas: RiskNeutral Pricing & Hedging Binomial Example; What’s Needed To Generalize Review of Probability  Basics 
ch. 1 

Jan. 28 
Review of Probability – Expectations, Convergence, Change of Measure 
ch. 1 

Feb. 4 
Information, Filtrations, Independence, Conditioning 
ch. 2 

Feb. 11 
Random Walk and Brownian Motion 
Sec. 3.13.3 

Feb. 18 
Properties of Brownian Motion 
Sec. 3.43.8 

Feb. 25 
Stochastic Calculus: Itô’s Integral, Itô’s Lemma 
Sec. 4.14.4.1 

March 3 
General Itô Lemma; Black–Scholes Equation 
Sec. 4.4.24.5 

March 17 
Multivariate Stochastic Calculus; Levy’s Criterion Girsanov’s Theorem: RiskNeutral Measure, BlackScholes Formula 
Sec. 4.6, 4.8 Sec. 5.15.2 

March 24 
Martingale Representation Theorem: Hedging Fundamental Theorems of Asset Pricing: existence and uniqueness of Risk Neutral Measure 
Sec. 5.35.4 

March 31 
Basic Applications to Financial Assets 
Sec. 5.55.7 

April 7 
Stochastic Differential Equations; FeynmanKac Thm. 
Sec. 6.16.6 

April 14 
Further Topics For Applying the Model 
TBD from Ch. 710 

April 21 
Further Topics For Applying the Model 
TBD 

April 28 
Further Topics For Applying the Model 
TBD 


Final Exam TBD week of May 5 to May 10 
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 chapters 7 thru 10, or a project that goes beyond what the text presents on a topic covered in chapters 1 thru 6. 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.