On distributional and asymptotic results for exponential functional of renewal -- reward processes describing risk models



Akahori, J, Constantinescu, C, Imamura, Y and Pham, Hh
(2020) On distributional and asymptotic results for exponential functional of renewal -- reward processes describing risk models.

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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: math.PR, math.PR
Depositing User: Symplectic Admin
Date Deposited: 28 Sep 2020 07:50
Last Modified: 05 Oct 2022 21:50
Open Access URL: https://www.tandfonline.com/doi/full/10.1080/03461...
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3102631