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On Distributional and Asymptotic Results for Exponential Functional of Renewal -- Reward Processes Describing Risk Models by Akahori, J.; Constantinescu, C.; Imamura, Y.; Pham, Hh. is a scholarly article available to read on EtoBox.

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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.

Author

Akahori, J.; Constantinescu, C.; Imamura, Y.; Pham, Hh.

Published

2020

Language

EN