We consider jump processes which has only downward jumps with size a fixed fraction of the current process. The jumps of the pro cesses are interpreted as crashes and we assume that the jump intensity is a nondecreasing function of the current process say $lambda$(X) (X = X(t) process). For the case of $lambda$(X) = $X^{alpha}$, $alpha$ > 0, we show that the process X shold explode in finite time, say $t_e$, conditional on no crash For the case of $lambda$(X) = (lnX)$^{alpha}$, we show that $alpha$ = 1 is the borderline of two different classes of processes. We generalize the model by adding a Brownian noise and examine the blow up properties of the sample paths.