IJPAM: Volume 78, No. 2 (2012)


Gert Beister$^1$, Bernd Luderer$^2$
$^1$Dreiserstr. 36, 12587 Berlin, GERMANY
$^2$Department of Mathematics
Chemnitz University of Technology
Chemnitz, 09107, GERMANY

Abstract. In [1] the authors presented a trading model, which enabled the description of typical movements of share values over the time. The basic assumptions are the dependence of temporal share value variation $W(t)$ on the daily buying stimulus, the ``stimulus velocity'' $dK(t)/dt$, and the distance between $W(t)$ and the basic share value $M$. The stimulus velocity itself was assumed to be proportional to the deviation of $W(t)$ from its personal expectation $S$. With these both assumptions an ``ordinary'' trading process was defined. Additionally, the possibility of ``disturbing activities'' was introduced, assuming their proportionality to the share value acceleration. The latter model was called a ``general'' trading process. Here, a modification of this model will be discussed, replacing the difference $W\!-\!M$ by its absolute value. In this way, the in [1] not easily explainable case of negative value velocity despite of positive daily buying stimulus can be prevented. Furthermore, it will be shown that the trading model can also be applied for simulations of DAX index time sequences.

Received: April 10, 2012

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

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

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 2