An Asymptotic Solution for the Free Boundary Parabolic Equations

In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the numerical solution as time is near to maturity.

• Hsuan-Ku Liu
• Ming Long Liu

• Integral equation
• asymptotic solution
• free boundary problem
• American exchange option.

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