asymmetric cost function for deep neural network binary classifier
Rather than 0 use 0.1 or some other small non-zero value. Use the true y as an indicator function, multiply your class probability by your reward component, and sum terms for all possibilities to get a usable loss, like this:

$Loss(y, y_p) = (1-y)(1)(y_p) + (y)(-0.7)(y_p) + (0.1)(1-y_p)$

Where $y_p =P(\hat{y}=1|X)$