Although stochastic models driven by latent Markov processes are widely used, the classical importance sampling method based on the exponential tilting method for these models suffers from the difficulty of computing the eigenvalue and associated eigenfunction and the plausibility of the indirect asymptotic large deviation regime for the variance of the estimator. We propose a general importance sampling framework that twists the observable and latent processes separately based on a link function that directly minimizes the estimator's variance. An optimal choice of the link function is chosen within the locally asymptotically normal family. We show the logarithmic efficiency of the proposed estimator under the asymptotic normal regime. As applications, we estimate an overflow probability under a pandemic model and the CoVaR, a measurement of the co-dependent financial systemic risk. Both applications are beyond the scope of traditional importance sampling methods due to their nonlinear structures.

翻译：尽管以隐马尔可夫过程驱动的随机模型被广泛使用，基于指数倾斜方法的经典重要性采样方法在应用于此类模型时，面临计算特征值与关联特征函数的困难，以及估计量方差的间接渐近大偏差机制的合理性问题。本文提出一个通用重要性采样框架，该框架通过一个直接最小化估计量方差的链接函数，分别对可观测过程与隐过程进行扭曲。我们选取局部渐近正态族中的最优链接函数。研究表明，在渐近正态机制下该估计量具有对数效率。作为应用，我们估算了流行病模型中的溢出概率以及CoVaR（一种衡量金融系统共同风险相依性的指标）。这两个应用场景因其非线性结构，均超出了传统重要性采样方法的适用范围。