On a Flexible Loan Repayment Method Depending on Borrower’s Asset with an Early Termination Clause

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. The repayment method can reduce the loan default probability, but it causes the uncertainty of the pay off time. Because the repayment term is related to the regular repayment amount in this method, a boundary for the regular repayment amount is set up in order to avoid too long repayment term. This will balance the benefit of borrowers and lenders and improve the applicability of this method. By establishing a mathematical model of the residual value of the loan, this model can be transformed into an initial-boundary problem of a partial differential equation. The analytic solution and the expected time to pay off the loan are obtained. Finally, numerical analysis are shown.