Speakers
for 2002/2003
Tuesday, April 1
Speaker: V.M. Rothos
Department
of Mathematics and Computer Science
University
of Leicester, England
Title: "Traveling
Kinks in discrete sine-Gordon lattices with an inter-site potential"
Abstract:
The existence of traveling kinks is studied analytical for discrete
sine-Gordon lattices with an inter-site potential. The reduced functional
differential equation is formulated as an infinite dimensional differential
equation which is reduced by a centre manifold method to a 4-dimensional
singular ODE with certain symmetries and with heteroclinic structure.
The bifurcations of solutions from heteroclinic ones are investigated
for singular perturbed systems.
Tuesday, March 18
Speaker: Peter
Forsyth
School
of Computer Science
University
of Waterloo
Title: "Robust
Numerical Methods for Contingent Claims under Jump Diffusion Processes"
Abstract:
It is well known that the standard Geometric Brownian motion model
of asset price evolution is flawed. An alternative approach is based
on a combination of Brownian motion and discontinuous jumps, which
seems to fit real data reasonably well. However, there has been very
little work on developing robust numerical methods for pricing options
under the assumption that the underlying assets follow a jump diffusion
process. In this talk, an implicit method is developed for discretization
of option pricing models which assume that the underlying process
is a jump diffusion. This method can be applied to a variety of contingent
claim valuations, including options with American early exercise,
uncertain volatility/ transaction cost models, and exotic options
(Asian, Parisian). Proofs of timestepping stability and convergence
of a fixed point iteration scheme are presented. For typical model
parameters, it is shown that the fixed point iteration reduces the
error by two orders of magnitude at each iteration. The correlation
integral is computed using an FFT method. Techniques are developed
for avoiding wrap-around effects. Numerical tests of convergence for
a variety of options are presented. This is joint work with Yann d'Halluin
and Ken Vetzal.
Tuesday, January 28
Speaker:
Robert Almgren
Mathematical
Finance Program
University
of Toronto
Title: "Competitive
Bids for Principal Trades"
Abstract:
In a principal trade, or risk bid, a broker undertakes to execute
a large portfolio transaction on behalf of a client, and the broker
is paid a fixed premium for assuming all the risk and costs associated
with the transaction. In previous work of Almgren and Chriss, and
in nonlinear extensions by Almgren, we showed how, by making reasonable
assumptions about market impact, optimal trading problems like this
one could be solved using a simple calculus of variations method rather
than dynamic programming. In this application, we use a Sharpe-ratio-like
measure to determine, *independently* of the broker's risk tolerance,
the minimum premium that the broker should demand in order for this
bid to be a competitive use of the firm's capital. We also determine
the optimal execution strategy if the bid is accepted.
[Joint work with N Chriss]
Tuesday,
November 26
Ian
Buckley
Imperial College, London, U.K.
University of Toronto, Canada
Title: "Portfolio optimization
with the Gaussian mixture distribution"
Abstract:
A tractable and practical generalization to Markowitz mean-variance
style portfolio theory is presented in which portfolios of assets,
in particular hedge funds and commodity trading advisors (CTAs), can
be handled successfully. Making the assumption that their returns
have the finite Gaussian mixture distribution and using the probability
of outperforming a target return as the objective function, these
assets are optimized in the static setting by solving a non-linear
programming problem to find portfolio weights. If the mixture distribution
has two Gaussian components, these can be associated with "tranquil"
and "distressed" states of the market.
Tuesday,
November 19
Dr. Gregory
V. Morozov
Department of Physics & Astronomy
McMaster University
Title: "Second-order
differential equations with periodic coefficients
and
their application to some physical problems"
Abstract:
Basic properties of the Hill equation d^2E(z)/dz^2+f(z)E(z)=0, f(z+d)
= f(z)
are considered. Numerical and approximate analytical methods for
construction of its solution are described. Some physical and engineering
problems where it is necessary to solve this equation are demonstrated.
As
a specific example, propagation of optical waves through a periodic
system
of dielectric layers (1-D photonic crystals) is considered in detail.
Francois Major
Departement d'Informatique et de Recherche Operationelle
Universite de Montreal
Title: "Determination
and Classification of RNA Fundamental Building Blocks"
Date: Tuesday, November 5
Time: 4:00 pm ***Please
note time change***
Room: HSC/4E20 (the red zone of the hospital) ***Please
note room change***
Abstract:
Structural graphs are used to represent RNA secondary and tertiary
structures. The minimal cycle basis of the large
ribosomal subunit structural graphs was determined and analyzed. Redundant
cycles were found, some of which correspond to structural and functional
motifs. New instances of the classical GNRA motif were found, but
two instances do not fit the GNRA sequence definition. A novel motif,
similar to the GNRA tetraloop, was identified, but is composed of
nucleotides from two independent strands. The environment of this
motif suggests that it plays a role in the stabilization of tertiary
contact by binding the minor groove of an adjacent helix . In this
presentation, I will introduce the RNA structrual graph, the minimal
cycle basis, the distance metric used in the clustering, and the results
of applying this approach to the large ribosomal subunit.
Scott Rodney
Department of Mathematics and Statistics
McMaster University
Title: "Properties of harmonic
functions satisfying applied elliptic problems"
Date: Tuesday, October 29
Time: 3:30 pm
Room: BSB/101
Shui Feng
Department of Mathematics and Statistics
McMaster University
Title: "Scaling Limit
of Some Interacting Particle Systems"
Date: Tuesday, October 22
Time: 3:30 pm
Room: BSB/101
