Abstract The aim of this paper is threefold. Firstly, we define the necessary quantities associated to the lumpability of a Markov chain and study their fundamental properties. Secondly, we examine the case of approximate lumpability of a non-lumpable Markov and an efficient method of minimizing the error in the approximation. Finally, we introduce a family of general minimization problems that can be approached using this method and examine applications in credit risk modelling, particularly under recent regulatory changes related to loan classification and provision calculations under IFRS 9.

中文翻译：

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符合国际财务报告标准 9 框架的马尔可夫链可集性和信用风险建模的应用

摘要 本文的目的有三个。首先，我们定义与马尔可夫链集总性相关的必要量并研究它们的基本性质。其次，我们研究了不可集总马尔可夫的近似集总性的情况以及最小化近似误差的有效方法。最后，我们介绍了一系列可以使用这种方法处理的一般最小化问题，并检查信用风险建模中的应用，特别是在与 IFRS 9 下贷款分类和拨备计算相关的近期监管变化中。