[grads] [Sem-coll] AM Dept. Colloquium 11/5

[Joe Millham]

Greetings all:

Please join us for the Applied Mathematics department colloquium on Monday,
Nov. 5 at 4:40pm in E1 Room 106.  Refreshments will be served 10-15 minutes
beforehand

Stephane Crepey of the University of Evry, France
"About the pricing equation in finance"
Monday, Nov. 5, 2007 4:40pm E1 Room 106

Abstract:
We consider the pricing equation in finance in a rather general
Jump–Diffusion Setting with Regimes (see [2, 3]). This model may be viewed
as a suitable generalization of the interacting Itˆo and Point Process model
considered by Becherer and Schweizer in [1] (we consider in effect an
interacting Itˆo–L´evy and Point Process model). But as opposed to the
set-up of [1] where linear reaction-diffusion systems of parabolic equations
(pricing equations of European Contingent Claims, from the point of view of
the financial interpretation) are considered from the point of view of
classic solutions, here the application we have in mind consists of more
general optimal stopping or optimal game problems (pricing equations of
American or Game Contingent Claims, see [2]) for which the related
reaction-diffusion systems typically do not have classic solutions (and even
less so, that there are also jumps in the Itˆo–L´evy component of our
model). This leads us to study solutions in the viscosity sense, using
related reflected BSDE techniques as the main tool. We establish in
particular the convergence of stable, monotone and consistent approximation
schemes to the unique viscosity solution of the pricing equation.


See you there!

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


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