论文标题
高维资产价格模型的低维近似
Low-dimensional approximations of high-dimensional asset price models
论文作者
论文摘要
我们考虑在尺寸中降低的高维资产价格模型，以降低问题定价背景下问题的复杂性或维度诅咒的影响。我们应用模型订单降低（MOR）以获得还原系统。先前已经对MOR进行了渐近稳定的控制随机系统，其初始条件为零。但是，随机微分方程建模价格过程是不受控制的，具有非零的初始状态，并且通常不稳定。因此，我们扩展了MOR计划，并结合了确定性系统已知的技术思想。这导致了提供良好路径近似值的方法。在解释了还原过程后，分析了近似的误差，并显示了算法的性能进行了几个数值实验。在“数字”部分中，指出了该算法的好处。
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.
