An application of risk theory to mortgage lending

IF 1.6 3区经济学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Scandinavian Actuarial Journal Pub Date : 2021-11-16 DOI:10.1080/03461238.2021.1995781

J. Akahori, C. Constantinescu, Y. Imamura, H. Pham

引用次数: 0

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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风险理论在抵押贷款中的应用

受日本双重债务问题的启发，即使他们的房子被灾难性事件摧毁，抵押人也必须支付剩余的贷款，我们通过更新奖励过程的指数函数来模拟贷款人的现金流。我们提出了贷款还款的附加保险，并分析了首次还款时间分布的渐近行为，该分布表示全额还款的概率。我们证明了贷款全额偿还的有限时间概率以指数速度收敛于无限时间概率。在一些具体的情况下，我们计算了无限时间概率的精确形式和相应的溢价。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Scandinavian Actuarial Journal MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-STATISTICS & PROBABILITY

CiteScore

3.30

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Scandinavian Actuarial Journal is a journal for actuarial sciences that deals, in theory and application, with mathematical methods for insurance and related matters. The bounds of actuarial mathematics are determined by the area of application rather than by uniformity of methods and techniques. Therefore, a paper of interest to Scandinavian Actuarial Journal may have its theoretical basis in probability theory, statistics, operations research, numerical analysis, computer science, demography, mathematical economics, or any other area of applied mathematics; the main criterion is that the paper should be of specific relevance to actuarial applications.