Although stochastic models driven by latent Markov processes are widely used, the classical importance sampling methods based on the exponential tilting for these models suffers from the difficulties in computing the eigenvalues and associated eigenfunctions 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 using 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. 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 features.

翻译：尽管由隐马尔可夫过程驱动的随机模型被广泛使用，但基于指数倾斜的经典重要性采样方法在处理此类模型时面临诸多困难：包括特征值及相关特征函数的计算难题，以及估计量方差在间接渐近大偏差体系下的合理性存疑。本文提出一种通用重要性采样框架，该框架通过链接函数分别对可观测过程与隐过程进行扭曲，以直接最小化估计量的方差。我们在线性渐近正态族中选取链接函数的最优形式，并证明所提估计量具有对数效率。在应用层面，我们分别估计了疫情模型下的溢出概率与衡量金融系统性风险共依赖性的CoVaR指标。由于这两类应用均具有非线性特征，传统重要性采样方法均无法有效处理。