IJPAM: Volume 68, No. 4 (2011)


Gert Beister$^1$, Bernd Luderer$^2$
$^1$Dreiserstr. 36, Berlin, 12587, GERMANY
e-mail: gert@beister.com
$^2$Department of Mathematics
Chemnitz University of Technology
Chemnitz, 09107, GERMANY
e-mail: bernd.luderer@mathematik.tu-chemnitz.de

Abstract. A mathematical method is presented, using functions stepwise defined over the time scale, which describes the development of share values on the base of detailed trading activities. Two simple relations, between the share value together with its temporal variation and the velocity or acceleration of trade stimulus, result in a non-linear first-order differential equation, even providing analytical solutions in the case of constant parameters. With this equation an ``ordinary'' trading process can be defined, illustrated by characteristic examples. For demonstrating the usefulness of the method, a calibration procedure on some time interval of the Frankfurt-Effekten-Fonds is demonstrated. Additionally to the ordinary trading process, ``disturbing'' activities can be taken into account, preferably in relationship to trade stimulus acceleration. In this way, a non-linear second-order differential equation results, whose solutions contain accelerated increases and diminished decreases of the share value during buying or selling, respectively. In both cases the implementation destructive process instabilities may occur, especially share value breakdowns. Some of the mathematical statements can serve as starting point for discussions from an economical point of view.

Received: February 14, 2011

AMS Subject Classification: 34A12, 91G80, 97M30

Key Words and Phrases: functional description of financial markets, forecast of share values, time series, hyperbolic functions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 68
Issue: 4