Let $V_t$ satisfy the SDE $dV_t = -\gamma V_t dt + \alpha dW_t$. Let $\tau$ be the first hitting time for 0, i.e., $\tau $ = min$(t | V_t = 0)$. Let $s =$ min$(\tau, 5)$. Let $\mathcal{F}_s$ be the $\sigma$-algebra generated by all $V_t$ for $t\leq s$. Calculate $G= E[V_5 ^2 | \mathcal{F}_s]$ by showing that it is given as a simple function of one random variable.
Found this on a practice final and really don't know how to start. I thought of a possible PDE approach using say the Kolmogorov Backward Equation, but does anyone know a possible alternative to tackle this problem? Any hint would be helpful. Thanks in advance.