一类自由边界问题解的渐近性

Critical Analysis for the Solution of Free Doundary Problem

讨论一类抛物积微分方程自由边界问题解的渐近性．利用偏微分方程的渐近性理论,证明在无界区域上一类抛物积微分方程自由边界问题的解,以及当时间趋于无穷大时,收敛于稳态的积微分方程自由边界问题的解．这一结论可用于解释期权定价中带跳扩散模型,当执行日期趋于无穷大时,美式期权价格及最佳实施边界收敛于永久美式期权价格及最佳实施边界．

The intent of this study is to discuss the critical property of a free boundary problem of a parabolic integro-differential equation. Using the critical theory of partial differential equation, we prove that the solution of a free boundary problem of parabolic integro-differential equation converges to the solution of a free boundary problem of integro-differential equation in limitless region when time run to infinite. Using this result, we can explain that the price and optimal exercise boundary of American option converge to the price and optimal exercise boundary of perpetual American option when the expiry date runs to infinite in a jump-diffusion model.