Importance sampling for option pricing with feedforward neural networks
研究如何用前馈神经网络计算合适的抽样测度，降低蒙特卡洛估计的方差，并用于路径依赖欧式期权定价，数值实验涵盖多种资产价格模型。
Abstract We study the problem of reducing the variance of Monte Carlo estimators through performing suitable changes of the sampling measure computed by feedforward neural networks. To this end, building on the concept of vector stochastic integration, we characterise the Cameron–Martin spaces of a large class of Gaussian measures induced by vector-valued continuous local martingales with deterministic covariation. We prove that feedforward neural networks enjoy, up to an isometry, the universal approximation property in these topological spaces. We then prove that sampling measures generated by feedforward neural networks can approximate the optimal sampling measure arbitrarily well. We conclude with a comprehensive numerical study pricing path-dependent European options for asset price models that incorporate factors such as changing business activity, knock-out barriers, dynamic correlations and high-dimensional baskets.