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SS 214 Mathematical Finance Course Web page: SYLLABUS                                                                                               

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Syllabus
Homeworks and Exams
Readings



SYLLABUS:

Instructor: Jaksa  Cvitanic, 137 Baxter,  x1784, cvitanic@hss.caltech.edu
Office Hours: Monday 3:30-4:00PM or by appointment.
Class meetings:  Mo,Wed 5:00-6:25PM, Baxter 125


Prerequisites: A solid knowledge of  probability, at a level of an upper level undergrad course.
Some exposure to stochastic processes, real analysis/measure theory and partial differential equations is
helpful, but not mandatory.

Grading:  40% homework, 60% exam or project or presentation.

Content and Goals:
 
This is an  introductory graduate course on Mathematical Finance.
The plan is to focus more on Financial Economics, as opposed to Financial Engineering
aspects, but this will depend on the interest of registered students.
 There are two main areas we will cover:

- 1. Pricing of options and other financial derivatives
- 2. Optimal portfolio selection

  In the first part, we will distinguish between complete markets, in which there will be
a unique no-arbitrage price, and incomplete markets, where absence of arbitrage is not
sufficient to obtain uniqueness of prices. We will start with discrete-time models, but most
of the course will be in the framework of continuous-time, Brownian Motion driven models.
An introduction to Stochastic, Ito Calculus will be given. The benchmark model will be the
Black-Scholes-Merton pricing model, but we will also cover more general models, such as
stochastic volatility models. Models with market frictions such as portfolio constraints will also
be considered. We will discuss both the Partial Differential Equations approach, and the Martingale
approach. They are related through the notion of Backward Stochastic Differential Equations and
the Feynman-Kac theorem.

  In the second part we will find optimal portfolio strategies in the above mentioned models, and
discuss relationship to pricing and risk management. The two parts are related through the concept of
risk-neutral probabilities (or equivalent martingale measures, or state-price densities).

READINGS:  The main textbook is

D. Duffie:  Dynamic Asset Pricing Theory, Third Edition.  2001.


However, we will not always follow the textbook closely.
We will use other books, lecture notes and research papers, too, such as:
 
J. Cvitanic "Theory of portfolio optimization in markets with frictions".    (Lecture Notes)

Students who are interested in additional computational and mathematical
aspects can also consult the following books:

J. Cvitanic and F. Zapatero: Introduction to the Economics and Mathematics of Financial Markets (introductory level)
S. Shreve: Stochastic Calculus for Finance II : Continuous-Time Models     (intermediate level)
T. Bjork:  Arbitrage Theory in Continuous Time  (intermediate/advanced level)
I. Karatzas and S. Shreve: Methods of Mathematical Finance   (advanced level)