For academics, for one possibility, look into
B-schools: At the research
universities, the B-school research requirement
seems to be to publish nearly anything.
Some of the journals popular in B-school
publishing have not very high standards for
quality.

The B-schools are basically
forced by some standards efforts
to teach some courses that
are essentially applied math.

One might guess that the B-schools
want to be professional or clinical
but, instead, they tend to want to
see themselves as applied social
science, and social science has
physics envy and wants to be
mathematical. Their favorite math
is linear statistics. So typically
there's a lot of such statistics
in the research at B-schools. And
typically the B-school profs are not
very good at math or statistics.

B-schools also want to dabble in
computing -- if you can teach some
courses in computing, even as electives,
then you might get liked for that.

No doubt some B-schools would like
someone who could teach courses
in financial engineering, say,
with Brownian motion, stochastic
integration, Black-Scholes
and generalizations -- basically
the Brownian motion solution to the
Dirichlet problem. So, if you
like mathematical finance, then
maybe teach it in a B-school.

DC may still be a good area for applied
math: So, submit a Civil Service application
and also send copies to the usual
suspects -- NIST, various DoE labs,
various DoD labs, various groups
interested in economics or mathematical
finance, that is, maybe the Federal
Reserve (also try the regional
Fed banks), the Social Security
Administration, etc. If you want,
try NSA, CIA, DIA, FBI, etc. -- no telling
what they might want to do with some
applied math. Also try the JHU/APL.

There have long been lots of
Beltway Bandit shops because
commonly Congress gives the
departments of the Federal Government
more money to spend than full time
head count to spend it on so that
a lot of the money and/or work goes through
companies. E.g., Edward Snowden
worked for Booz-Allen or some such.

For technical jobs around DC,
it used to be that the job ads in
The Washington Post were good
places to look.

There is a chance that Google, Facebook,
Yahoo and some others are interested
in some projects that might
be able to use some high end applied math.
A problem may be that the other workers there are
not very good at math and, really,
make a mess out of the work, the
opportunities, the positions, etc.,
and that can be bad for everyone.

It's not clear that everything
in mathematical finance is
a rat race. I doubt that James
Simons ran a rat race shop.

Houston has some important slots for
optimization, e.g., as in the work
of Princeton Chem Eng prof Floudas.
E.g., here's all the crude oil
inputs we have available and the costs,
and here's all the prices for
all the possible refinery products.
So, say what crude oil to buy and what
products to sell to maximize
earnings. That's an old problem,
but likely people are still working
on it.

The airlines have some very serious
problems in fleet and crew scheduling,
and first cut it's integer linear
programming. But with uncertainties,
if you want to handle them at all realistically,
the formulations and solutions can become
challenging in all respects.
A better solution can show
its value just on the computer
and get taken seriously. For
some airline spending $100
million a month just on jet fuel,
saving a few percent can pay for
some nice computing, work, etc.

Maybe look at what the operations
research people are doing these
days in scheduling for trucks,
airplanes, cargo ships, etc.

No doubt Amazon, Wal-Mart, etc.
have some good problems
that are generalization of
the old transportation
problem -- the one Kantorovich
got a Nobel prize for.
Now we regard that problem
as least cost flows on a network
and use the simplex algorithm
to solve it and where a basic
feasible solution corresponds to
a spanning tree of arcs on the network.

My view is that broadly now being
handy with probability and
probabilistic modeling of real
situations is valuable, not that
you can expect anyone else to know this
so that, really, all you can sell
are results, not the work.

E.g., with the Kolmogorov
definition of a random variable,
a function from a measurable space
to the reals measurable with respect
to the Borel subsets of the reals
and a sigma algebra on the measurable
space, go get a number, any number,
and then regard it as the value of
a random variable, that is,
intuitively, one number among
others that might have been
observed. Now you know the first
step in analyzing any given
data -- call each number the
value of a random variable.
Then look for some assumptions,
independence, orthogonality,
or other relationships among
the random variables.
Keep the weak law of large numbers
at your side -- that is, get
some independent, identically
distributed samples and take
an average. There's more!
Uh, the set of all real
valued random variables
X so that E[X^2] is finite
forms a Hilbert space. The
inner product is (X,Y)
= E[XY]. So, yup, that
completeness holds is a bit
amazing, but it does and the
proof is mostly just the Minkowski
inequality from the inner product.
Then in a Hilbert space we can
do projections, and they
are approximations, e.g., least
squares.

Currently the Internet
ad people and their
ad targeting should be an
opportunity to do some valuable
applied math.

For what to study beyond the usual
ugrad and Master's pure/applied
math, I'd say the math sciences,
the math of operations research
or systems analysis or electronic
engineering. So, linear algebra,
numerical linear algebra,
linear systems of various kinds,
optimization (linear, integer linear, non-linear,
network linear programming),
etc.

My view is that soon computing will
run aground due to running
out of any additional utility
from just their usual intuitive
and heuristic approaches to solving
practical problems and need
math. But don't hold you breath.

Maybe you can have a good, long
term career, say, long enough to
have kids and get them through college,
at some one organization. Maybe.
Maybe for some DoD lab. Maybe.

Otherwise I have to suspect that
in the end you will have to
be a businessman where you
think of the product/service,
develop it, deliver it to your
customers, and get the revenue.
Then you get to use whatever math
helps without trying to talk
some non-mathematical manager
into letting you try,
and then you just deliver the
results, not the math itself,
to your customers.

In the short term, I'd suggest
get a job for a salary,
keep one foot in pure/applied
math, keep the other foot in
computing, try to make a
career out of the job,
but really expect to have to do,
and, thus, to look
for a way to do, a startup
based on applied math and
computing. There you just
use the math as an advantage,
maybe the crucial core --
still the rest that is more
routine is also important.

For how "lucrative", essentially
that's up to you!
Broadly, can't really
expect someone else to
create a good job in applied
math for you. Instead, you
have to create the job you
want and then take that job,
do well with it, and build
a career. You can do this
starting a pizza shop;
with math and computing,
they should be advantages.
E.g., with some abstract
algebra applied to coding
theory, A. Viterbi built
Qualcomm.

If you know someone who knows someone,
then maybe could get into some
niche slot somewhere, maybe on the
staff of a committee of Congress.