a stochastic cobweb dynamical model
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ID: 242947
2008
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Abstract
We consider the dynamics of a stochastic cobweb model with linear demand and a backward-bending supply curve. In our model,
forward-looking expectations and backward-looking ones are assumed, in fact
we assume that the representative agent chooses the backward predictor with probability
๐_,__0_๐_1, and the forward predictor with probability (1โ๐), so that the expected price at time ๐ก is a random variable and consequently the dynamics describing the price evolution in time is governed by a stochastic dynamical system. The dynamical system becomes a Markov process when the memory rate vanishes. In particular, we study the Markov chain in the cases of discrete and continuous time. Using a mixture of analytical tools and numerical methods, we show that, when prices take discrete values, the corresponding Markov chain is asymptotically stable. In the case with continuous prices and nonnecessarily zero memory rate, numerical evidence of bounded price oscillations is shown. The role of the memory rate is studied through numerical experiments, this study confirms the stabilizing effects of the presence of resistant memory.
| Reference Key |
brianzoni2008discretea
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|---|---|
| Authors | ;Serena Brianzoni;Cristiana Mammana;Elisabetta Michetti;Francesco Zirilli |
| Journal | Journal of the American Heart Association |
| Year | 2008 |
| DOI |
10.1155/2008/219653
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| URL | |
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