An application of risk theory to mortgage lending

Jiro Akahori, C. Constantinescu, Y. Imamura and H. H. Pham

Scandinavian Actuarial Journal, 2022, vol. 2022, issue 5, 447-469

Abstract: 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.

Date: 2022
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DOI: 10.1080/03461238.2021.1995781

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