Interests
I am a Professor in the
Mathematics
and Computer Science Department at
Santa Clara University. Yes, that means
I do math just because I like it. The doctors tell me that many people
with my condition can still lead an active, normal life. Personally, I suspect
these doctors are a bunch of quacks.
I am an Applied
Mathematician and study Partial Differential Equations that arise in
Finance, Engineering, Chemistry, Economics, and Physics.
Recently, I have concentrated on issues from Financial
Mathematics and Economics.
Jonathan Goodman and I have worked on
linear partial differential
equations
that describe how to price stock options. We have also analyzed the
effect
of transaction costs on optimal investment strategies. Tom Wong and I
have studied optimal investment strategies in the presence of taxes,
in
particular quantifying the effect of reaping tax losses wherever
possible. (The
C++ program for quantifying these losses is available
here.)
Dan Friedman and I have looked at
the effect of gradient based dynamics on models arising in Economics and other fields.
Jim DiLellio
and I are looking at how in retirement to drain IRA, Roth IRA, and taxable stock accounts in the
most tax efficient manner possible.
I have also
studied non-linear, first order hyperbolic partial differential
equations called Conservation Laws and
Hamilton-Jacobi equations. I have shown how to use these equations to
study shape from shading, which reconstructs a 3-D surface by
exploiting
a 2-D picture (or radar image) of the surface, and chromatography,
which
is a chemical separation process.
For more, see my publications list here.
