Seminars and Colloquia by Series

A weak convergence for Approximation of American Option Prices

Series
CDSNS Colloquium
Time
Thursday, April 22, 2010 - 16:00 for 1 hour (actually 50 minutes)
Location
Skile 255
Speaker
Prof. Weiping Li – Oklahoma State University
Based on a sequence of discretized American option price processes under the multinomial model proposed by Maller, Solomon and Szimayer (2006), the sequence converges to the counterpart under the original L\'{e}vy process in distribution for almost all time. We prove a weak convergence in this case for American put options for all time. By adapting Skorokhod representation theorem, a new sequence of approximating processes with the same laws with the multinomial tree model defined by Maller, Solomon and Szimayer (2006) is obtained. The new sequence of approximating processes satisfies Aldous' criterion for tightness. And, the sequence of filtrations generated by the new approximation converges to the filtration generated by the representative of L\'{e}vy process weakly. By using results of Coquet and Toldo (2007), we give a complete proof of the weak convergence for the approximation of American put option prices for all time.

A sufficient condition for the continuity of permanental processes with applications to local times of Markov processes

Series
Stochastics Seminar
Time
Thursday, April 22, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Jay Rosen – College of Staten Island, CUNY
We provide a sufficient condition for the continuity of real valued permanental processes. When applied to the subclass of permanental processes which consists of squares of Gaussian processes, we obtain the sufficient condition for continuity which is also known to be necessary. Using an isomorphism theorem of Eisenbaum and Kaspi which relates Markov local times and permanental processes we obtain a general sufficient condition for the joint continuity of the local times.

Interpretation of some integrable systems via multiple orthogonal polynomials

Series
Analysis Seminar
Time
Wednesday, April 21, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Dolores Barrios – Polytechnical University of Madrid
Some discrete dynamical systems defined by a Lax pair are considered. The method of investigation is based on the analysis of the matrical moments for the main operator of the pair. The solutions of these systems are studied in terms of properties of this operator, giving, under some conditions, explicit expressions for the resolvent function.

A uniqueness result for the continuity equation in dimension two

Series
PDE Seminar
Time
Tuesday, April 20, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Gianluca Crippa – University of Parma (Italy)
In the simplest form, our result gives a characterization of bounded,divergence-free vector fields on the plane such that the Cauchyproblem for the associated continuity equation has a unique boundedsolution (in the sense of distribution).Unlike previous results in this directions (Di Perna-Lions, Ambrosio,etc.), the proof does not rely on regularization, but rather on adimension-reduction argument which allows us to prove uniqueness usingwell-known one-dimensional results (it is indeed a variant of theclassical method of characteristics).Note that our characterization is not given in terms of functionspaces, but using a qualitative property which is completelynon-linear in character, namely a suitable weak formulation of theSard property.This is a joint work with Giovanni Alberti (University of Pisa) andStefano Bianchini (SISSA, Trieste).

A panorama of elliptic curves

Series
Research Horizons Seminar
Time
Tuesday, April 20, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Douglas Ulmer – Professor and Chair, School of Mathematics

Please Note: Hosted by: Huy Huynh and Yao Li

Elliptic curves are solution sets of cubic polynomials in two variables. I'll explain a bit of where they came from (computing the arc length of an ellipse, hence the name), their remarkable group structure, and some of the many roles they play in mathematics and applications, from mechanics to algebraic geometry to cryptography.

High order numerical methods for differential equations with singular sources

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 19, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Jae-Hun Jung – Mathematics, SUNY Buffalo
Solutions of differential equations with singular source terms easily becomenon-smooth or even discontinuous. High order approximations of suchsolutions yield the Gibbs phenomenon. This results in the deterioration ofhigh order accuracy. If the problem is nonlinear and time-dependent it mayalso destroy the stability. In this presentation, we focus on thedevelopment of high order methods to obtain high order accuracy rather thanregularization methods. Regularization yields a good stability condition,but may lose the desired accuracy. We explain how high order collocationmethods can be used to enhance accuracy, for which we will adopt severalmethods including the Green’s function approach and the polynomial chaosmethod. We also present numerical issues associated with the collocationmethods. Numerical results will be presented for some differential equationsincluding the nonlinear sine-Gordon equation and the Zerilli equation.

Test - RT 159125

Series
Other Talks
Time
Saturday, April 17, 2010 - 13:07 for 4 hours (half day)
Location
158
Speaker
All Around Nice Guy – Buddy and Pal –
Abstract expressionism is a post–World War II art movement in American painting, developed in New York in the 1940s. It was the first specifically American movement to achieve international influence and put New York City at the center of the western art world, a role formerly filled by Paris.

The Faber-Krahn problem for the Hamming cube

Series
Combinatorics Seminar
Time
Friday, April 16, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Alex Samordnitsky – Professor, Hebrew University (Jerusalem, Israel)
The Faber-Krahn problem for the cube deals with understanding the function, Lambda(t) = the maximal eigenvalue of an induced t-vertex subgraph of the cube (maximum over all such subgraphs). We will describe bounds on Lambda(t), discuss connections to isoperimetry and coding theory, and present some conjectures.

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