论文标题
使用罚款迭代解决自由边界问题的高级递延校正方法，并向美国选项定价应用
A high-order deferred correction method for the solution of free boundary problems using penalty iteration, with an application to American option pricing
论文作者
论文摘要
本文提出了一种高级递延校正算法，结合了使用四阶有限差方法解决自由和移动边界问题的罚款迭代。通常，当在固定的计算网格上解决自由边界问题时，即使使用了高阶方法，解决方案的订单也很低。使用详细的误差分析，我们观察到，可以通过依次纠正有限差系统来将解决方案收敛顺序提高到第四阶，其中校正是从先前计算的下级较低级解决方案得出的。鉴于良好的初步猜测，罚款迭代迅速汇聚。我们使用多个示例证明了算法的准确性和效率。数值结果表明，我们的算法给出了解决方案和自由边界位置的四阶收敛。我们还针对富有挑战性的美国PUT期权定价问题测试了我们的算法。我们的算法给出了预期的高阶收敛。
This paper presents a high-order deferred correction algorithm combined with penalty iteration for solving free and moving boundary problems, using a fourth-order finite difference method. Typically, when free boundary problems are solved on a fixed computational grid, the order of the solution is low due to the discontinuity in the solution at the free boundary, even if a high-order method is used. Using a detailed error analysis, we observe that the order of convergence of the solution can be increased to fourth-order by solving successively corrected finite difference systems, where the corrections are derived from the previously computed lower order solutions. The penalty iterations converge quickly given a good initial guess. We demonstrate the accuracy and efficiency of our algorithm using several examples. Numerical results show that our algorithm gives fourth-order convergence for both the solution and the free boundary location. We also test our algorithm on the challenging American put option pricing problem. Our algorithm gives the expected high-order convergence.
