Feeds:
Posts

## BELLMAN’S EQUATION FOR OPTIMAL CONTROL PROBLEMS

### Zulfikar Ahmed<canshoahsurvivereally@gmail.com>

11:02 AM (2 minutes ago)

 to bookprize, bookprize, chomsky, dws, hj, roberto, vlad, Jewel, Judit, Shamim, Toby, aimee, Ronald, Eniah, Raul, strivergreen, sfwithin, ritualaddiction, donoho
Optimal Control theory deals with control of processes defined by an ordinary differential equation.

d/dx f(t) = A( f(t), a(t))

f(t_0) = A_0
The problem is to tamper with the second variable in A, a(t), to optimize some functional of f, an objective function that in control theory is called a PAYOFF function.  There is a large theory for these with many applications in economics.  The substance of this theory is based on a solvable approach to these types of problems by Richard Bellman by dynamic programming.  In other words in the discrete case the Bellman equation and in the continuous case the Hamilton-Jacobi-Bellman equation and solving these is the substance of the discipline.  See attached paper of Bellman for some idea.
Our problem of interest is a still hypothetical one which we have great hopes for: we would like to model global volatility on a mathematical graph where every node is a traded asset and we would like to find some partial differential equation of the form

(d/dt – Laplacian) u = F(u)
where F(u) is not homogeneous such as V(x)u(x,t) (where x is a graph vertex in our case) but rather something more nonlinear.  So the optimal control problem, which we now just think about in a wishy-washy manner until ideas clarify on how to formalize it for careful solution, is this:  the dynamics of volatility, assuming correct, produces various storms that impact seven billion of our people every day.  So what optimal control problem can we formulate and solve in this case which would allow some shelter to the human race from these storms?

Obviously these are preliminary and vague ideas that require more thought.  I’m going to just throw it out there for now and simply formulate the conjecture that properly formulated there exists a control theory problem that could be used to manage these volatility storms without challenging the positive civilizational benefits of legitimate trade that is a human affairs constant with far deeper roots in our civilizations than the cheap dogmatism of Marxism.  Trade and merchant routes are great things.  I can buy today cheap trunks from Chinamen in San Francisco that would otherwise make my poverty stricken life worse for having given local San Francisco boutiques that charge \$150 for a hat much more than I can afford without trade.  The fundamental responsibility of true science is to be physicians of a gigantic human collective, not to be totalitarian big brothers spying on everyone or treating people like criminals in their own country — I am more American than most of these plebian hicks with rifles who have never read Emerson damn it.  What sort of science would not consider the PHENOMENON of scientific effects of global financial volatility not to be the terrible human suffering caused by the financial volatility storms?  Scientists and science were developed partly by wars and so on but what necessity was there from 1945 to declare war on the entire human race by fabricating a Cold War by two military poles from Washington (and no this is not hot air you can ask the famous insider Gore Vidal he wrote about this clearly I’ve a blog quoting him:  https://zulfahmed.wordpress.com/2011/05/27/gore-vidals-story-of-the-cold-war/).  So we have a lot of scientists working on interesting problems for the ultrawealthy but we don’t have yet a legitimate science of finance or of global volatility.

The point of this note is to ask whether optimal control theory can be applied to a network model of volatility dynamics to determine some reasonable methods of taming the volatility storms.  Obviously this is not a trivial question but it is my sacred duty to ask the question, and it is always fun when “VEE ASK ZEE QWESTIONS FOR A CHANGE” you know?

Attachments area