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

Abstract:

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.

Key words:repayment method;remaining loan value;expected clear off time;free boundary problem;shooting method