CONVERGENCE OF A LEAST‐SQUARES MONTE CARLO ALGORITHM FOR AMERICAN OPTION PRICING WITH DEPENDENT SAMPLE DATA
分析了Longstaff-Schwartz算法在使用单一重复利用的独立蒙特卡洛样本路径时的收敛性，证明了对于有限VC维的L2函数集的随机误差估计，并给出了神经网络等非线性非凸集的整体误差界。
Abstract We analyze the convergence of the Longstaff–Schwartz algorithm relying on only a single set of independent Monte Carlo sample paths that is repeatedly reused for all exercise time‐steps. We prove new estimates on the stochastic component of the error of this algorithm whenever the approximation architecture is any uniformly bounded set of L 2 functions of finite Vapnik–Chervonenkis dimension (VC‐dimension), but in particular need not necessarily be either convex or closed. We also establish new overall error estimates, incorporating bounds on the approximation error as well, for certain nonlinear, nonconvex sets of neural networks.