  Inspired by the double-debt problem in Japan where the mortgagor has to pay
the remaining loan even if their house was destroyed by a catastrophic event,
we model the lender's cash flow, by an exponential functional of a
renewal-reward process. We propose an insurance add-on to the loan repayments
and analyse the asymptotic behavior of the distribution of the first hitting
time, which represents the probability of full repayment. We show that the
finite-time probability of full loan repayment converges exponentially fast to
the infinite-time one. In a few concrete scenarios, we calculate the exact form
of the infinite-time probability and the corresponding premiums.
