论文标题
非常重要的采样
Deep Importance Sampling
论文作者
论文摘要
我们提出了一种通用路径依赖性的重要性采样算法，其中Girsanov诱导的路径空间上的概率变化由一系列神经网络表示，以轨迹的过去为输入。在每个学习步骤中，对神经网络的参数进行了训练，以减少通过这种度量变化引起的蒙特卡洛估计量的方差。这允许措施的一般路径依赖性变化，可用于减少任何依赖路径的财务收益的方差。我们在数值实验中表明，对于由呼叫和呼叫和看台的不对称组合，呼叫和拨号的不对称组合组合的回报，多息票和单个优惠券的对称组合，我们能够减少2和9之间的蒙特卡洛估计差异。培训可以离线进行，只每周更新。
We present a generic path-dependent importance sampling algorithm where the Girsanov induced change of probability on the path space is represented by a sequence of neural networks taking the past of the trajectory as an input. At each learning step, the neural networks' parameters are trained so as to reduce the variance of the Monte Carlo estimator induced by this change of measure. This allows for a generic path dependent change of measure which can be used to reduce the variance of any path-dependent financial payoff. We show in our numerical experiments that for payoffs consisting of either a call, an asymmetric combination of calls and puts, a symmetric combination of calls and puts, a multi coupon autocall or a single coupon autocall, we are able to reduce the variance of the Monte Carlo estimators by factors between 2 and 9. The numerical experiments also show that the method is very robust to changes in the parameter values, which means that in practice, the training can be done offline and only updated on a weekly basis.
