27th April 2005, Wednesday
Title : Risk-Neutral Option Pricing for Log-Uniform Jump-Diffusion
Model.
Speaker : Zongwu Zhu.
Affiliation : MSCS, UIC.
Where : 636 Science and Engineering Offices (SEO).
When : 4:00 pm.
ABSTRACT
A reduced European call option pricing formula by risk-neutral valuation
is given. It is shown that the European call and put options for jump-diffusion
models are worth more than that for the Black-Scholes (diffusion) model with
the common parameters. Due to the complexity of the risk-neutral jump-diffusion
results, obtaining a closed option pricing formula like that of Black-Scholes
is not viable. Instead, a Monte Carlo algorithm, including optimal control
variates, is used to compute European option prices. Monte Carlo variance
reduction techniques are enhanced by the use antithetic random variates.
The numerical results show that this is practical, efficient and easily
implementable algorithm.
26th April 2005, Tuesday
Title : The effect of gravity modulation on the onset of filtrational
convection.
Speaker : Natalya Popova.
Affiliation : MSCS, UIC.
Where : 512 Science and Engineering Offices (SEO).
When : 4:15 pm.
ABSTRACT
In the present talk we will consider the effect of vertical vibration
on
the onset of convection in an infinite horizontal layer of fluid saturating
a porous medium. The mathematical model is described by equations
of
filtrational convection in the Darcy-Oberbeck-Boussinesq approximation.
Linear analysis of the stability of the quasi-equilibrium state is performed
by using Floquet theory with the employment of the method of continued
fractions. The limiting case of high frequency vibration is investigated
using the method of averaging, and the case of low frequency vibration
-
using the WKB method. It is concluded that, by means of changing parameters
of vibration (the frequency and the amplitude), we can control convective
instability in a layer of fluid saturating a porous medium.
30th March 2005, Wednesday
Title : BioEngineering Applications of Fractional Calculus.
Speaker : Professor Richard L. Magin.
Affiliation : Professor and Head, Department of BioEngineering, UIC.
Where : 636 Science and Engineering Offices (SEO).
When : 4:00 pm.
ABSTRACT
Fractional calculus (integral and differential operations of non-integer
order) is not often used to model biological systems. Although the basic
mathematical ideas were developed in the 17th century by
the mathematicians Leibniz (1695), Liouville (1834) and Riemann (1892),
and brought to the attention of the engineering world by Oliver Heaviside
in the 1890s, it was not until 1974 that the first book was published on
the topic by Oldham and Spanier. Several recent conferences have highlighted
the application of fractional calculus in continuum mechanics, diffusion
theory and electromagnetics, but not much activity is ongoing in bioengineering.
This is surprising since the methods of fractional calculus when defined
as a Laplace or Fourier convolution product are suitable forsolving many problems
in biomedical research. For example, early studies by Cole (1933) and Hodgkin
(1946) of the electrical properties of nerve cell membranes and propagation
of electrical signals are well characterized by differential equations of
fractional order. The solution involves a generalization of the exponential
function to the Mittag-Leffler function, which provides a better fit to the
observed cell membrane data. A parallel application of fractional derivatives
to viscoelastic materials establishes, in a natural way, hereditary integrals
and the power law (Nutting/ Scott Blair) stress-strain relationship for biomaterials.
In this seminar, I will introduce the idea of fractional operations by following
the original approach of Heaviside, demonstrate the basic operation on well-behaved
functions (step, ramp, pulse, sinusoid) of engineering interest, and give
specific examples from physics, bioengineering and
biophysics. The fractional derivative accurately describes natural phenomena
that occur in such common engineering problems as heat transfer, electrode-electrolyte
behavior, and sub-threshold nerve propagation. By expanding the range of
mathematical operations to include fractional calculus, we can develop new
and potentially useful functional relationships for modeling biological systems
in a direct and rigorous manner.
17th
November 2004, Wednesday
Title : Spatial Solitons in Quasi-Phase-Matched Quadratic Media.
Speaker : Edward D. Farnum.
Affiliation : University of Washington.
Where : 712 Science and Engineering Offices (SEO).
When : 5:00 pm.
ABSTRACT
In non-linear optics, there are two broad categories of materials, which
exhibit entirely different phenomena. In quadratic materials, we see second
harmonic generation, and in cubic materials we can see an effect called self
focusing. Recently, there has been interest in trying to get "cubic-like"
effects, like self-focusing, from quadratic materials. In this talk I 'll
give a quick overview of what's been done, talk about a multiple scales approach
I've working on, and then look at some slow evolution results froma variational
point of view. 29th
October 2004, Friday
First organizational meeting of the student chapter.
Agenda : Discuss aspects of the activities of the chapter and to select
the chapter officers.
Where : 712 Science and Engineering Offices (SEO).
When : 4:30-5:30 pm.
EVERYONE
is welcome to attend
Last updated: Wednesday, 11-Apr-2012 23:28:26 CDT
