最小二乘蒙特卡罗法的稳定性
On the Stability the Least Squares Monte Carlo
摘要：
考虑Longstaff和Schwartz（2001）提出的用于美式证券定价的最小二乘蒙特卡罗（LSM）算法。该算法基于通过最小二乘问题将延拓值投影到某组基函数上。我们分析了算法的稳定性时，行使日期的数量增加，并证明，如果股票价格的基本过程是连续的，那么回归问题是病态的时间参数的小值。
英文摘要：
Consider Least Squares Monte Carlo (LSM) algorithm, which is proposed by Longstaff and Schwartz (2001) for pricing American style securities. This algorithm is based on the projection of the value of continuation onto a certain set of basis functions via the least squares problem. We analyze the stability of the algorithm when the number of exercise dates increases and prove that, if the underlying process for the stock price is continuous, then the regression problem is ill-conditioned for small values of the time parameter.
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