traded. The price evolution of this stock, assuming that $S=S(t_0)$ at $t=t_0$, is the following: $$S(t)=S(t_0)+ \int_{t_0}^{t}\mu(t')S(t')  dt' +\int_{t_0}^{t}\sigma(t') S(t') dW(t'-t_0),\label{dS}$$ where $W(t)$ is a Wiener process, a one dimensional Brownian motion with zero mean and variance equal to $t$. The drift, $\mu$, and the volatility, $\sigma$, are stochastic quantities whose initial values are $\mu_a$ and $\sigma_a$. After $t_0$ they may simultaneously change to different fixed values, $\mu_b$ and $\sigma_b$, but such a transition can take place only once in a lifetime: $$\mu(t)=\mu_a {\mathbf 1}_{t\leq \tau} +\mu_b {\mathbf 1}_{t>\tau},
$$ $$\sigma(t)=\sigma_a {\mathbf 1}_{t\leq \tau} +\sigma_b {\mathbf 1}_{t>\tau}.
$$ Throughout the text ${\mathbf 1}_{\{\cdot\}}$ will denote the indicator function, which assigns the value 1 to a true statement, and the value 0 to a false statement. Note that if $\sigma_a \neq \sigma_b$, we will have a market model with stochastic volatility. The case in which $\mu_a \neq \mu_b$ has in principle a more flexible interpretation, although we will concentrate our attention in the existence of two different (continuous in time) dividend pay-off regimes: $$\delta(t)=\delta_a {\mathbf 1}_{t\leq \tau} +\delta_b {\mathbf 1}_{t>\tau}.$$ These magnitudes are stochastic because the instant $\tau>t_0$ in which the transition occurs is a random variable. We will assume that 