The mortgage problem

Abstract

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>or=0, they show a lower bound r= Omega (/sup 1nM///sub (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+/sup 2///sub m+1/)(m+2). For other values of m, M the on-line policy is proven to be r/sup 2/-competitive.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>