An application of risk theory to mortgage lending

Akahori, J, Constantinescu, C, Imamura, Y and Pham, HH (2022) An application of risk theory to mortgage lending. SCANDINAVIAN ACTUARIAL JOURNAL, 2022 (5). pp. 447-469.

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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.

Item Type:	Article
Uncontrolled Keywords:	Exponential functional, renewal-reward process, ruin probability, double-debt problem, Fredholm integro-differential equation, stochastic fixed-point equation
Depositing User:	Symplectic Admin
Date Deposited:	28 Sep 2020 07:50
Last Modified:	18 Jan 2023 23:31
DOI:	10.1080/03461238.2021.1995781
Open Access URL:	https://www.tandfonline.com/doi/full/10.1080/03461...
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3102631