We consider high-dimensional asset price models that are reduced in their dimension in order to reduce the complexity of the problem or the effect of the curse of dimensionality in the context of option pricing. We apply model order reduction (MOR) to obtain a reduced system. MOR has been previously studied for asymptotically stable controlled stochastic systems with zero initial conditions. However, stochastic differential equations modeling price processes are uncontrolled, have non-zero initial states and are often unstable. Therefore, we extend MOR schemes and combine ideas of techniques known for deterministic systems. This leads to a method providing a good pathwise approximation. After explaining the reduction procedure, the error of the approximation is analyzed and the performance of the algorithm is shown conducting several numerical experiments. Within the numerics section, the benefit of the algorithm in the context of option pricing is pointed out.
翻译:我们考虑了高维资产价格模型,这些模型的尺寸已经降低,以减少问题的复杂性或在选择定价方面对维度的诅咒的影响。我们应用了减少订单的模型(MOR)来获得一个减少的系统。以前曾研究过对零初始条件下的无症状稳定的控制抽查系统。然而,模拟价格过程的随机差异方程式不受控制,具有非零初始状态,而且往往不稳定。因此,我们扩展了确定性系统已知的摩尔办法,并结合了确定性系统已知的技术概念。这导致了一种提供良好路径近似的方法。在解释了减少程序之后,对近似错误进行了分析,并展示了算法的运行情况进行了数性实验。在数字一节中,指出了选择定价背景下算法的好处。