crashes. In fact, process [**B**]{} yields akin crises. After the crash occurs, this drastic event might switch the system back to a $s\ge 0$ regime.

Final remarks {#Sec:final}
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We have analyzed stochastic models of a quite general form, with algebraic restoring force and algebraic multiplicative noise. A further generalization with the inclusion of an extra source of noise, of standard Wiener type, has also been analyzed. These additive-multiplicative processes are built on the basis of realistic features: The multiplicative noise describes innovations generated by endogenous mechanisms that amplify or attenuate a random signal, depending on the internal state of the system. Whereas, the additive noise encodes a direct influence of external random fields such as news or spontaneous fluctuations due to speculative trading. One of the goals of this work was to study systematically the PDF asymptotic solutions of these generalized models. We have shown that the inclusion of additive noise gives rise to new PDF shapes, with a richer spectrum of cross-over behaviors and, in particular, two-fold power-law decays. The shapes of the PDFs are governed by the effective market rules parametrized by $r$ and $s$. These parameters describe the algebraic nature of the global mean-reverting strength of 