The average behaviour of financial market by 2 scale homogenisation

Details The average behaviour of financial market by 2 scale homogenisation The average behaviour of financial market by 2 scale homogenisation

2006-08-18

arxiv.org/abs/physics/0608191v1

Physics

Physics and Society

To be published in Acta Phys. Pol. B

Scientific paper

The financial market is nonpredictable, as according to the Bachelier, the mathematical expectation of the speculator is zero. Nevertheless, we observe in the price fluctuations the two distinct scales, short and long time. Behaviour of a market in long terms, such as year intervals, is different from that in short terms. A diffusion equation with a time dependent diffusion coefficient that describes the fluctuations of the financial market, is subject to a two-scale homogenisation, and long term characteristics of the market such as mean behaviour of price and variance, are obtained. We indicate also that introduction of convolution into diffusion equation permits to obtain L- stable behaviour of finance.

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