Jrising at 19:04, 29 February 2012

2012-02-29T19:04:35Z

New page

Apply dynamic programming to the problem of
optimal control of policy levers within a complex system. I don't
think it's inherently the most interesting topic or applies the most
material from class, but it serves my larger research projects. I'm
not sure how far I can get analytically, and a lot of the work may
turn out to be numerical and heuristic, but this paper would be a
combination of some literature review, some analytic work, some
algorithms, and some simulations (maybe empirical results).

The basic analytic setup is to assume that the state of a system in
time is some large set of functions, <math>{S_i(t)}</math>. The policy lever is
l(t), and can change the state variables by various functions, <math>\frac{dS_i}{dt}
= f_i({S_i(t)}, l(t))</math>. Then I can reinterpret the fundamental
optimization problem, max over <math>l(t)</math> of integral of <math>u({S_i(t)}, l(t)) *
exp(-\delta t)</math> into the high-dimensional dynamic programming problem,
<math>V({S_i}) = \max_{l_t} u({S_i}, l_t) + (1 / (1 + \delta)) * V({S_i
+ dt * f_i(l_t)})</math>.

Analysis of Leverage - Revision history

Jrising at 19:04, 29 February 2012