Neural Network-Based System for Currency Flow Planning

K. Pashkovskaya, V. Pavlov, and Arkady Borisov
Department of Decision Support Systems, Technical University of Riga, Latvia

Abstract

Let a firm have money resources available in several currencies. In times the firm needs to make payments in the required currency thus spending a part of these resources. The following information is available:

1. amount of money available in each currency at the firm's account;
2. courses of currency changes , for periodicity of twenty four hours;
3. the schedule of payments in the form of a sequence of pairs , , where is the date of payment, is the size of payment, ;
4. the schedule of money entry in the form of sequence of pairs , , where is the date of payment, is the size of payment, .

It is required to have amounts of money available in times according to the schedule of payments.

The problem is solved using two models: a model of currency course forecast and a combinatorial model of possible exchange pairs.

Solving the problem. The tree of states

First, let us build a tree of states. Let each level of the tree correspond to a certain pair (specific payment), i.e., the number of tree levels equals to the number of analysed payments. The root of the tree is initial state ( : is the current state of the money account). Nodes of the first level are alternative transformations of this state that are aimed to ensure required amount of money, , by time . Similarly, nodes of the k-th level are alternative transformations of states of the (k-1)th level.

Since the firm has only three kinds of currency: , , , the following situations may occur before the regular payment:

1. Two of three required currencies are available in sufficient amount (say, and ). In this situation the firm faces the choice: surplus of which currency should be used in the first instance in order to cover the shortage of the third currency.
2. Only one of three currencies is available in sufficient amount. Here, only the date of currency exchange should be determined. This situation could be represented constructing a level of the tree.
3. Available resources in each currency are sufficient for making payments in required currency. Then transformation operators are not applied to the current state.
4. Neither currency is available in sufficient amount. In this case the schedule of payments is assumed to be changed.

If situation (1) or situation (2) appears, the date of exchange and amount of sold/bought currency are determined. Let currency be required to be changed for currency . Then the minimal correlation of courses should be determined. It means that greatest possible amount of currency should be received for less possible amount of sold currency.

The date of exchange of the currency required by time , , could lie in interval . Currency exchange courses for the near future are considered to be known from the forecast.

To solve the above problem, a back-propagation neural network is proposed to use that applies an algorithm which was most spread in recent years, that is the error back-propagation algorithm. This algorithm was intended as an effective learning procedure, where transformation of the type "input-output" contains both rules and exclusions and it, in principle, suits for solving any non-linear classification problem.

When solving the above problem a multilayer neural network was used with the architecture 4-8-1 (that is, four neurons in input layer, eight neurons in the hidden layer and one neuron in the output layer). Such network architecture ensured satisfactory precision of forecast both for turning-points and for specific meanings of currency courses within the whole required time interval (from 5 to 20 days).

Since the number of maximum possible transformation for each state equals 2, the constructed tree is binary. Dimension of goal states G is equal to , where n is the number of tree levels. A set of transformation operators, F, is represented by currency exchange courses.

Solving of the problem consists in choosing the best variant, that is the goal state, which the greatest amount of money in each currency corresponds to, and obtaining a sequence of transformation operators for states from set F.

References

1

Winston, P. H., 1984. Artificial Intelligence. Addison-Wesley Publishing Company, Reading, Massachusetts.

2

Refenes, A. N., M. Azema-Barac, L. Chen, and S.A. Karoussos, 1993. `Currency Exchange Rate Prediction and Neural Network. Design Strategies'. Neural Computing & Applications.