TwoFuzzies....You and I?
Maybe not!
I tried to find something in your statement I could pick on but I failed.
The AIMWAY process is reactive. Exactly as you say it is. This poses the question:
Are Reactive Algorithms by definition impossible to optimise/analyse in a rigorous mathematical way?
At the danger of repeating myself:
I believe not, but I do know it beats me as to how to do it. I still believe that it is the discontinuous nature of the functions as we use them that makes it difficult. Essentially we are dealing with point functionsand that makes it elusive. Even if we formulate the value function on a continuous smooth price curve(curve fitting on the price data) we can not remove the discontinuities that result from the buying and the selling.
Also the stepwise updating of the PC and the discontinuities due to cash inputs/withdrawals add s complexities.
I see the problem clearly now, and on a clear day I might see all the way to the end of it.Still, the practical aspects are not easy to fathom.
Suppose we define the AIM structure in a completely differentiable and integratable set of functions as to how the value(or profit) changes with the smooth input. For as long as no sells or buys are introduced and no cash is added or withdrawn the system is analysable with normal techniques( or rather, with techniques that are familiar to me).
The AIM would function as is it was a process in a factory(my stomping ground).
OK, on this set of functions and various variables etc. we analyse it as we please and draw all sorts of conclusions as we please. If now any discontinuous even takes place the treatment ends there on that limiting case. OK, we simple redefine the new situation and fix the current endpoint as the start-punt for the next period. Also, the we do no longer look back onto the old situation but we simply take the endpoint-conditions and carry them forward as costs, accumulated profit, new parameters, etc. and start again from scratch. Historic data remains available and we can, if we wanted to, use that for current parameter optimisation.
To define the objectives for the studies is a piece of cake(anything is legit).
The process I have defined sounds a lot easier now. In fact is exactly the process I have defined for my Vortex Method except that in that process there are no explicit continuous functions defined. When I have presented the value function as a straight proportionality of time I in fact can model that as a time dependant function of a smooth stock price:
Stock Price(x) = ax
Stock Value(ax) = F1(ax)
Profit Function(F2(ax))=F1(ax) – Investment
No Problem. The functions will contain all the parameters that make up the value as well as the profit at any point in x, which is at any point in time of course as well. The entire purpose in my Vortex Method was to formulate an algorithm that would iteratively process the information from an identical starting point each time a change was made. From this point of view, if the Algorithm was a conscious being it would not ever know is it had just started the first cycle or the millionth cycle. This is how the Vortex Method works. In any case this system blindness does not mean that it is necessary for the process we are discussing. It simply is an aspect of the iterative nature that I see as required for a formal treatment of the discontinuous functions.
I think I will leave this as it is now. The process for a formal treatment appears all of a sudden rediculously simple for actually doing something like that.
I appreciate any comments on this, as after we have defined the functions then the questions becomes: what are we going to analyse in a rigorous mathematical way?
Take the road less traveled. It will make all the difference
The road I travel on is aready empty. Either I am on a road that leads nowhere or there beautiful vistas to be found. Anyway, I am not stuck in the traffic jam on the highway.
Conrad
AI
