具有违约边界的基于借贷人资产的贷款还款方式研究
Modeling on a Flexible Loan Repayment Method Based on the Borrower’s Asset with Boundary

研究在设定还款边界的条件下，还款强度依赖于借贷人资产的灵活的贷款还款方式。还款边界的设立可以防止出现由于定期还款额过少，导致还款期限过长的情况，平衡借贷双方利益。通过运用结构化方法的思想，对剩余贷款期望价值建立数学模型，并将其转换为偏微分方程的初边值问题，求解得到借贷人剩余贷款价值的解析表达式和期望还清贷款所需时间与其他参数之间的隐函数关系式。最后分析了各个参数对期望还清贷款时间的影响。
Aiming at the problem that the asset's fluctuation influences the borrower's repayment ability, a loan with a new and flexible repayment method is designed, which depends on the asset value of the borrower. In detail, the repayment due is the proportion of the present value of the borrower's asset. In order to avoid too little the repayment due and too long repayment period, a boundary for the repayment due is set up. This repayment method can reduce the loan default probability. But it causes the uncertainty of the pay off time. By establishing a mathematical model of the residual value of the loan, this repayment method with the boundary can be transformed into an initial-boundary value problem of a partial differential equation. The analytic expression of the residual loan value and the expected time to pay off the loan are calculated. Finally, numerical analyses are shown.