The mortgage problem

Mortgage refinancing is a complex real-life problem involving a sequence of decisions, each of which requires a trade-off between the transaction cost associated with refinancing and the benefit of obtaining a lower interest rate. The authors present a simplified mathematical model of this problem. Within this model, they seek to determine the best possible competitive ratio achievable by an on-line mortgage refinancing policy. The main results are the following: under the assumption that the initial mortgage is obtained with an interest rate M and that future interest rates cannot decrease below m⩾0, they show a lower bound r=Ω(^1nM /_(m+1)lnlnM) on the competitive ratio of any mortgage refinancing policy. Then they give an on-line policy that is optimal in some special cases, including the cases m=0 and M<(1+²/_m+1)(m+2). For other values of m, M the on-line policy is proven to be r²-competitive