Victor Nistor
The $K$-groups and the index theory of certain comparison $C^*$-algebras.
Wed, 05/12/2010 - 15:01 — SomNambulAuthors: Victor Nistor, Bertrand Monthubert
Subjects: K-Theory and Homology
AbstractWe compute the $K$-theory of comparison $C^*$-algebra associated to a
manifold with corners. These comparison algebras are an example of the abstract
pseudodifferential algebras introduced by Connes and Moscovici \cite{M3}. Our
calculation is obtained by showing that the comparison algebras are a
homomorphic image of a groupoid $C^*$-algebra. We then prove an index theorem
with values in the $K$-theory groups of the comparison algebra.Closed form asymptotics for local volatility models.
Wed, 10/14/2009 - 11:04 — SomNambulAuthors: Nick Costanzino, Victor Nistor, Wen Cheng, John Liechty, Anna Mazzucato
Subjects: Pricing of Securities
AbstractWe obtain new closed-form pricing formulas for contingent claims when the
asset follows a Dupire-type local volatility model. To obtain the formulas we
use the Dyson-Taylor commutator method re- cently developed in [7, 8, 10] for
short time asymptotic expansions of heat kernels, and obtain a family of
general explicit closed form approx- imate solutions for both the pricing
kernel and derivative price. We also perform analytic as well as a numerical
error analysis, and compare our results to other known methods.Approximate Solutions to Second Order Parabolic Equations I: analytic estimates.
Fri, 10/09/2009 - 18:27 — SomNambulAuthors: Radu Constantinescu, Nick Costanzino, Anna L Mazzucato, Victor Nistor
Subjects: Analysis of PDEs
AbstractWe establish a new type of local asymptotic formula for the Green's function
of a parabolic linear operator with non-constant coefficients. Our procedure
leads to an elementary, algorithmic construction of approximate solutions to
parabolic equations which are accurate to arbitrary prescribed order in the
short-time limit.
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