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Escaping the Brownian stalkers. (English) Zbl 1190.60078
Summary: We propose a simple model for the behaviour of longterm investors on a stock market. It consists of three particles that represent the stock’s current price and the buyers’, respectively sellers’, opinion about the right trading price. As time evolves, both groups of traders update their opinions with respect to the current price. The speed of updating is controlled by a parameter; the price process is described by a geometric Brownian motion. We consider the market’s stability in terms of the distance between the buyers’ and sellers’ opinion, and prove that the distance process is recurrent/transient in dependence on the parameter.
MSC:
60J65 Brownian motion
60K10 Applications of renewal theory (reliability, demand theory, etc.)
91G20 Derivative securities (option pricing, hedging, etc.)
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