[grads] [Sem-coll] AM Dept Seminars & Colloquium This Coming Week

[Joe Millham]

Greetings all:
Please join us for the following Applied Mathematics Department Seminars &
Colloquium the week of Fri 11/9 - Fri 11/16.  Please remember:  Attendance
by graduate students to all AM dept. seminars is highly recommended.  
Refreshments will be served before the talks.

------------------------------------------------------

Discrete Applied Mathematics Seminar
Friday 11/9 - Kathryn Nyman of Loyola University - Chicago
E1 103 3:00 pm
Title: Descent Algebras, rising sequences, and a good card trick done
poorly, if at all
Abstract Below

Stochastics and Computation Seminar
Monday 11/12 - Aijun Du of IIT AM Graduate Program
E1 129 12:45 pm
Title: Deviation, Ergodicity, and Reduction for Stochastical Dynamical
Systems

AM Dept Colloquium & Mathematical Finance Seminar
Monday 11/12 - Erhan Bayraktar of University of Michigan
E1 106 4:40 pm
Title: On the Finite Horizon American Option Pricing Problem:  A Proof of
Smoothness and an Exponentially Fast Converging Scheme
Abstract Below

------------------------------------------------------

Discrete Applied Mathematics Seminar
Friday 11/9 - Kathryn Nyman of Loyola University - Chicago
E1 103 3:00 pm
Title: Descent Algebras, rising sequences, and a good card trick done
poorly, if at all
Abstract:  We will take a short look at how one might model card shuffling
with permutations. This leads to a study of the descent algebra, and finally
we will introduce a subalgebra (close to my heart) known as the peak
algebra. We find a lovely connection between the peak algebra and descent
algebra and explore some of its properties.



AM Dept Colloquium & Mathematical Finance Seminar
Monday 11/12 - Erhan Bayraktar of University of Michigan
E1 106 4:40 pm
Title: On the Finite Horizon American Option Pricing Problem:  A Proof of
Smoothness and an Exponentially Fast Converging Scheme
Abstract:  We give a new proof of the fact that the value function of the
finite time horizon American put option for a jump diffusion, when the jumps
are from a compound Poisson process, is the classical solution of a
quasi-variational inequality and it is $C^1$ across the optimal stopping
boundary. Our proof only uses the classical theory of parabolic partial
differential equations of Friedman and does not use the theory of vicosity
solutions, since our proof relies on constructing a sequence of functions,
each of which is a value function of an optimal stopping time for a
diffusion. (Also, the previous proof holds only for a certain range of
parameters.) The sequence is constructed by iterating a functional operator
that maps a certain class of convex functions to smooth functions satisfying
variational inequalities (or to value functions of optimal stopping problems
for a geometric Brownian motion). The approximating sequence converges to
the value function exponentially fast, therefore it constitutes a good
approximation scheme, since the optimal stopping problems for diffusions can
be readily solved using the well-know numerical schemes such as SOR.


See you there!

Joe Millham
Administrative Assistant
Applied Mathematics Department
312.567.8984
jmillham at iit.edu 

_______________________________________________
sem-coll mailing list
sem-coll at math.iit.edu
http://math.iit.edu/mailman/listinfo/sem-coll