Your example doesn't involve discounting at all. Your nonlinearities are in the probabilities, not the payoffs.

Hyperbolic discounting says that you're willing to plan to give someone a loan at rate P starting a month from now, but when the time arrives you change your mind about what the fair rate is. Not change your mind in response to new evidence about the probability of defaulting, but predictably change your mind in the absence of any new arguments, just because event X a month from now has different utility to you than event X now.