论文标题
关于更新的指数功能的分配和渐近结果 - 描述风险模型的奖励过程
On distributional and asymptotic results for exponential functional of renewal -- reward processes describing risk models
论文作者
论文摘要
受到日本双人双重问题的启发，即使他们的房屋被灾难性事件摧毁了他们的房屋，我们也必须支付剩余的贷款，我们通过更新奖励流程的指数功能对贷方的现金流进行了建模。我们建议偿还贷款的保险附加方式，并分析第一次打击时间分布的渐近行为，这代表了全额还款的可能性。我们表明，全额贷款偿还的有限时间概率将指数级汇合到无限的时间。在一些具体的情况下，我们计算了无限时间概率和相应溢价的确切形式。
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.
