论文标题
有多少个内部模拟，以最小二乘蒙特卡洛计算有条件的期望？
How many inner simulations to compute conditional expectations with least-square Monte Carlo?
论文作者
论文摘要
用最小二乘蒙特卡洛计算条件期望E [f（y）| x]的问题至关重要，并且已经被广泛研究。要解决这个问题，通常假定一个Y的样本与X的样本一样多。但是，当通过计算机模拟生成样品，可以模拟Y的条件定律时，它可能与X的$ N值相关。对于X的每个样品，$ n值y y y y y y y y y y y y y y值的x $ n值为X的每个样品的$ n值。目前的工作确定了给定计算预算的最佳价值，并估算出k的最佳价值。主要取消信息是，计算增益可能更重要的是，对于采样X的计算成本，给定X的计算成本很小。X的计算成本。关于K的最佳选择和计算利益的数值插图在不同的示例中给出了计算增益，包括一个受风险管理的启发。
The problem of computing the conditional expectation E[f (Y)|X] with least-square Monte-Carlo is of general importance and has been widely studied. To solve this problem, it is usually assumed that one has as many samples of Y as of X. However, when samples are generated by computer simulation and the conditional law of Y given X can be simulated, it may be relevant to sample K $\in$ N values of Y for each sample of X. The present work determines the optimal value of K for a given computational budget, as well as a way to estimate it. The main take away message is that the computational gain can be all the more important that the computational cost of sampling Y given X is small with respect to the computational cost of sampling X. Numerical illustrations on the optimal choice of K and on the computational gain are given on different examples including one inspired by risk management.
