2020/09/23 by Jirô Akahori, Corina Constantinescu, Akahori, J. +5
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2009.11167
openalex publication_date 2020/09/23 · openalex created_date 2020/10/01 · openalex updated_date 2026/07/28
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.