一种依赖借贷人资产的灵活还款方式的贷款的设计和研究

Design and Study of a Loan with Flexible Repayment Which Relies on the Borrower’s Assets

摘要: 针对借贷人资产的波动影响还款能力的问题，设计了一种还款强度依赖于借贷人资产的新的贷款还款方式，即俗称的“有多少还多少”方式。这种还款方式减少了违约的可能却带来了还清贷款所需时间的不确定性。通过对剩余贷款价值建立数学模型，将贷款的剩余价值看成借款人资产的未定权益，并将其转换为偏微分方程的终值问题，求解得到公司剩余贷款价值的解析式和期望还清贷款所需时间，最后对结果进行了数值模拟分析。

Abstract: Aim at the uncertainty of a kind of assets, which affects the borrower’s repayment ability, a new loan is designed, whose repayment depends on the borrower’s assets. This method reduces the possibility of default, but brings the uncertainty of the clear off time of the loan. By establishing a mathematical model of the residual loan value, the residual value of the loan is regarded as the undetermined equity of the borrower’s assets, which is converted into the final value problem of partial differential equation. The analytic solutions for residual loan value and clear off time of the loan are obtained. Finally, the parameters are analyzed and calculated numerically.