The Math Colloquium at CSUSM
Talks in Spring 2004
The Colloquium meets on Mondays from
1:00 to 2:00 p.m. in Room 337A, Science Hall 2.
If you would like to give a talk, please
contact Radhika Ramamurthi.
An e-mail announcement is sent out on Fridays before talks with the abstract
--- if you would like to be on the mailing list, please send
e-mail to Carrie Dyal.
Abstracts
COMING UP soon
An introduction to the Mathematics of Pricing Stock Options
by Amber Puha, CSUSM Math.
In 1997, Robert Merton and Myron Scholes received the Nobel prize for their
work on pricing securities derivatives. An example of a securities derivative
is European call option, which is a contract that gives the owner the right,
but not the obligation, to purchase a specific security
(e.g., a particular stock) at a set time for a set price. By trading such an option,
an investor can
hedge against the risk associated with market volatility. For example,
suppose that an investor believes that the price of a certain stock will
be high at some time in the future. Rather than purchasing the stock,
the investor could instead purchase a call option. Then, the investor
can decide whether or not to exercise the option based on the actual stock price.
Pricing securities derivatives emerged as an important concern in the late 1960's and early 1970's
when a relaxation in the regulations allowed insurance companies
and banks to invest in the derivatives market. At about that time, two
economists, Fisher Black and Myron Scholes, developed a mathematically based pricing strategy,
which Robert Merton later simplified and expanded.
This work had a profound impact on the trading practices in financial markets worldwide.
Sadly, Black passed away prior to 1997, and therefore was ineligible to be a co-Nobel prize recipient.
In the talk, we will examine a simplified version of this body of work.
In particular, we will analyze the single period Cox-Ross-Rubenstien (CRR) model
using some of the key principles and methodologies that Black, Scholes, and Merton
developed to construct their derivatives pricing theory.
Despite the fact that this model is very simple, the analysis will illustrate certain
essential aspects of their Nobel prize winning work such as dynamic hedging and the risk
neutral probability measure.
An introduction to complex analysis of several variables
by Marshall Whittlesey, CSUSM Math.
Students of complex analysis learn that differentiable (i.e. analytic)
functions with respect to a complex variable possess certain exotic
features not typically present in functions of real variables. In this
talk I will describe how even more exotic features lie unexpected in
several complex variables. Among these are Hartogs' 1906 discovery that
analytic continuation is much more common in several variables, and
Poincare's discovery the same year that the Riemann Mapping theorem does
not hold in higher dimensions.
This talk requires some knowledge of complex analysis; students who have
taken Math 536 will find that knowledge sufficient to understand the talk.
Abstracts from previous weeks
Number Theory and Galois Theory
by Jessica Jones, CSUSM Math.
Galois sought to distinguish the polynomial equations which can be solved by a formula from those which cannot. Galois theory later developed into a study of the behavior of field extensions. I will discuss Galois theory and reveal its usefulness to other areas of mathematics, particularly Number Theory. For example, Galois theory can be used to prove Quadratic Reciprocity and portions of Fermatbs Last Theorem. We will focus our attention on extensions of the rational numbers and I will introduce a significant result, the Kronecker-Weber Theorem, which is obtained when the extensions are Abelian.
Questions/Comments:
(ramamurt(at)csusm(dot)edu)
Last modified: Sep. 18,2003