Multicurrency advisor based on the NSW model. Detailed description and perspectives

Previous works have brought about [1][2][3] great response and some incomprehension of the results obtained. Partially, it is fault of the author's striving to present the material in a possibly compact form without dealing much with details and peculiarities of the algorithms. Also, it is important that financial mathematics is not the science the natural scientists are used to -it has somewhat different method of proof and strictness, and frequently anything, which seems to be natural in the theoretical physics, or in the theory of non-linear differential equations, is not known or is not too popular in the financial statistics.

As well, there are some difficulties with respect to terminology: incorrect, or not fully legal, иor too broad use of some terms having clear enough and strict interpretation. The most unlucky happened to be such an ordinary notion as fractal, etc.

Mention should be made that complications of problems connected with financial forecasts have rather serious grounds. Apart from having very complicated structure featuring multiple nonlinearities and feedbacks, financial system interacts with real economy segment, whose behavior, though connected with the financial component, in many respects is determined by its own peculiarities: cyclicity, limited resources, successes and problems of the scientific and technical progress, political, cultural, and educational components, influences exerted by world market, etc.

With this, according to the author’s opinion, solution of the problem is significantly facilitated by the fact, that the problem does not consist in modeling of complicated natural process, but only modeling of the decision making process of the Forex market subjects possessing the same input information, together with comparable computational and analytical possibilities aimed at rather definite and, generally speaking, simple objective. Great physicist А. Einstein once said: «Everything should be made as simple as possible, but not simpler».

This was the principle, as well as the principle of maximum accessibility for non-mathematicians, which governed the author when writing this work.

Further we will consider financial sequences in discrete time representation. Let us confine ourselves, for purposes of for definiteness, to the Forex market. For the Forex market it is usually assumed that at the n t time the following values are known : opening prices, closing prices, minimum and maximum price values, prices and volumes of transactions for formation of time frame with period, as well as current (tick-by-tick) value of currency pairs quotations and, thereby, tick-by-tick value for all time interval n t t t … , 1 0 .

For beginning let us confine ourselves to consideration of parameters pertaining to the formed time frame, and let us construct from them any linear combination, e.g. half-sum of the opening -closing prices, or some combinations of the opening and closing prices, and maximum and minimum for this time frame.

This discrete time series n X in future will be called initial series. It is significant that we can simultaneously construct several such series for all or part of currency pairs traded at the Forex market. That is actually we have a discrete vector series.

Subsequent analysis requires setting of basic hypothesis and exact formulation of the problem being solved.

Let us formulate the problem as follows: firstly, at what time it is necessary to enter long or short position (i.e. to buy or to sell currency pair), and secondly, in case initial deposit of a preset value is available, how it should be distributed among various currency pairs to attain maximum trade efficiency, which will be understood as maximum current profit with moderate risk [ 2 ].

Initially, for the purpose of simplicity, we will consider an unidimensional sequence. As a basic hypothesis let us assume that all (here I underline it -all) information necessary for making of efficient decision is contained in the quotations history, that is in the initial sequence n X . By the way, thereby we reject necessity to use so-called fundamental analysis when making the decision.

The last statement is of course debatable, but since we are going to construct exact or maximally quantitative decision making procedure, this assumption has very serious grounds. Firstly, the fundamental analysis results can hardly be evaluated qualitatively, and it is difficult to range weight and evaluate contribution of each of them, secondly, even when they have any grounds, their effect extends to essentially more broad forecasting horizons than that necessary for the decision making, and finally, the fundamental analysis data will in that our other measure influence current quotations or input variables, which, in one way or another, will be analyzed.

In other words, by letting the market himself to «digest» the fundamental forecasts, we will make decisions on the grounds of available information. The same

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