A stochastic model for speculative bubbles
Résumé
The aim of this paper is to provide a simple modelling of speculative bubbles and to derive some quantitative properties of its dynamical evolution. Starting from a description of individual speculative behaviours, we build and study a second order non-reversible Markov process, which after simple transformations can be viewed as a turning two-dimensional Gaussian process. Then, our main problem is to obtain some bounds for the persistence rate relative to the return time to a given price. In our main results, we prove with both spectral and probabilistic methods that this rate is almost proportional to the turning frequency \omega of the model and provide some explicit bounds. In the continuity of this result, we build some estimators of \omega and of the pseudoperiod of the prices. At last, we prove the existence of the persistence rate and of the associated quasi-stationary distribution.
Origine : Fichiers produits par l'(les) auteur(s)
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