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

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

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arXiv · 2009.11167

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

J. Akahori·C. Constantinescu·Y. Imamura·Hh. Pham

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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.

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J. Akahori, C. Constantinescu, Y. Imamura, Hh. Pham. 2020-09-23. On distributional and asymptotic results for exponential functional of renewal -- reward processes describing risk models. https://arxiv.org/abs/2009.11167

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