Adaptive Control Variates for Finite-Horizon Simulation
Adaptive Control Variates for Finite-Horizon Simulation
复制标题
有限范围仿真的自适应控制变量
DOI：
10.1287/moor.1070.0251
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
S. Henderson
中科院分区：
文献类型：
--
作者：
Sujin Kim;S. Henderson
自适应蒙特卡罗方法是一种提高仿真效率的技术，旨在自适应地调整仿真估计器。自适应蒙特卡罗方法的大部分工作都致力于自适应调整重要采样方案。我们转而关注基于控制变量方案的自适应方法。介绍了两种自适应控制变量方法，并给出了它们的渐近性质。第一种方法使用随机逼近自适应调整控制变量估计量。它很容易实现，但需要对参数进行一些重要的调优。第二种方法是基于样本平均近似。不再需要调优，但它在计算上可能会很昂贵。最后给出了障碍期权定价的数值结果。
Adaptive Monte Carlo methods are simulation efficiency improvement techniques designed to adaptively tune simulation estimators. Most of the work on adaptive Monte Carlo methods has been devoted to adaptively tuning importance sampling schemes. We instead focus on adaptive methods based on control variate schemes. We introduce two adaptive control variate methods, and develop their asymptotic properties. The first method uses stochastic approximation to adaptively tune control variate estimators. It is easy to implement, but it requires some nontrivial tuning of parameters. The second method is based on sample average approximation. Tuning is no longer required, but it can be computationally expensive. Numerical results for the pricing of barrier options are presented to demonstrate the methods.