依赖借款方资产的还款方式中的自由边界问题  

A Free Boundary Problem in Flexible Repayment Method Based on Borrower’s Assets

作　　者：梁进[1] 张柳青 LIANG Jin;ZHANG Liuqing(School of Mathematical Sciences,Tongji University,Shanghai 200092,China)

机构地区：[1]同济大学数学科学学院,上海200092

出　　处：《同济大学学报（自然科学版）》2022年第2期291-298,共8页Journal of Tongji University:Natural Science

基　　金：国家自然科学基金(12071349)。

摘　　要：考虑一种依赖借款方资产的灵活还款方式,通过设置资产边界将借款方资产分为高资产区域以及低资产区域,并在两个区域中设定不同的还款条款,由此建立了高低资产区域内剩余贷款价值所满足的带限制的自由边界问题模型。采用显示差分格式以及打靶法求解了自由边界和期望还清贷款时间,最后讨论了模型参数对期望还清贷款时间的影响。结果表明:期望还清贷款时间和各参数间存在单调关系。A flexible repayment method based on the borrower’s asset is considered.By introducing a predetermined asset boundary,the borrower’s asset is divided into high and low asset regions.A restricted free boundary problem model for the remaining loan value is established via different repayment terms in two regions.The explicit finite difference method and shooting method are applied to solve the free boundary and the expected clear off time of the loan.Finally,the influence of the model parameters on the expected clear off time is discussed.The results show that there is a monotonic relationship between the expected clear off time and these parameters.

关 键 词：还款方式 剩余贷款价值 期望还清贷款时间 自由边界问题 打靶法 

分 类 号：F830[经济管理—金融学]