An asymptotic method to a financial optimization problem

Abstract

This paper studies the borrower's optimal strategy to close the mortgage when the volatility of the market investment return is small. Integral equation representation of the mortgage contract value is derived, then used to find the numerical solution of the free boundary. The asymptotic expansions of the free boundary are derived for both small time and large time. Based on these asymptotic expansions two simple analytical approximation formulas are proposed. Numerical experiments show that the approximation formulas are accurate enough from practitioner's point of view. © 2010 Springer Science+Business Media B.V.