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An application of risk theory to mortgage lending

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Listed:
  • J. Akahori
  • C. Constantinescu
  • Y. Imamura
  • H. H. Pham

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.

Suggested Citation

  • J. Akahori & C. Constantinescu & Y. Imamura & H. H. Pham, 2022. "An application of risk theory to mortgage lending," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2022(5), pages 447-469, May.
    • Handle: RePEc:taf:sactxx:v:2022:y:2022:i:5:p:447-469
    DOI: 10.1080/03461238.2021.1995781
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