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 who studies Optimal Control problems and Partial Differential
Equations that
arise in Finance, as well as in Engineering, Chemistry, Economics,
and Physics.
My recent research has concentrated on issues in Financial Mathematics and Economics.
- Sanjiv Das
and I have worked with Franklin
Templeton investments on a string of papers that
show people how to optimally change investments over time to maximize their chance of attaining a goal
or how to optimally change investments and optimally
select which goals to obtain when they have multiple goals over time of different importance
to them. One of the offshoots of this
work has been Franklin Templeton's
Goals Optimiation Engine (GOE).
- Jim
DiLellio
and I have looked at how a retiree can drain IRA/401(k), Roth IRA/Roth 401(k), and taxable stock accounts in
the most tax efficient manner possible.
- Jonathan Goodman and I have analyzed the effect of
transaction costs
on optimal investment strategies and worked on partial differential
equations
that describe how to price stock options.
- Dan Friedman and I have looked at
the effect of gradient based
dynamics on models arising in Economics and other fields.
- 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.)
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.
Many of my publications can be found here.
