论文标题
使用基于优化的模型订单降低来解决高维的最佳停止问题
Solving high-dimensional optimal stopping problems using optimization based model order reduction
论文作者
论文摘要
由于需要计算有条件期望的计算，因此通过高维度向后诱导解决最佳停止问题通常是非常复杂的。通常，此类计算基于回归，这种方法遭受了维数的诅咒。因此，本文的目的是为大规模资产价格模型建立缩小方案，并在降低的设置中解决相关的最佳停止问题（例如百慕大选项定价），其中回归是可行的。所提出的算法基于线性随机微分方程之间的误差度量。我们为减少系统系数建立了此误差措施的最佳条件，并提出了一种满足这些条件至小偏差的特定方法。我们在几个数值实验中说明了我们方法的好处，其中确定了百慕大期权价格。
Solving optimal stopping problems by backward induction in high dimensions is often very complex since the computation of conditional expectations is required. Typically, such computations are based on regression, a method that suffers from the curse of dimensionality. Therefore, the objective of this paper is to establish dimension reduction schemes for large-scale asset price models and to solve related optimal stopping problems (e.g. Bermudan option pricing) in the reduced setting, where regression is feasible. The proposed algorithm is based on an error measure between linear stochastic differential equations. We establish optimality conditions for this error measure with respect to the reduce system coefficients and propose a particular method that satisfies these conditions up to a small deviation. We illustrate the benefit of our approach in several numerical experiments, in which Bermudan option prices are determined.
