基于违约风险模型的泊松过程教学设计

Instructional Design for the Poisson Process Based on a Default Risk Model

摘要: 泊松过程是最简单的一类计数过程，在实际生活中有着广泛的应用，一些复杂的计数过程借助某些变换也可以简化成泊松过程的情形进行考虑。然而，在高校随机过程课程的教学安排中，泊松过程相关内容的讲解往往比较抽象，导致学生对这部分知识的理解比较浅显，难以有效培养其理论应用能力。本文以住房抵押贷款违约模型的构建为具体案例，采用理论与应用相结合的教学方法，将泊松过程的定义与性质融入建模实践，逐步推进学生对泊松过程的学习。在此过程中，学生的逻辑思维能力，以及运用所学理论知识解决实际问题的能力均得到了锻炼。

Abstract: The Poisson process is the simplest type of counting process and is widely used in practice. Even complex counting processes can often be simplified to the form of a Poisson process through appropriate transformations. However, in the teaching of the stochastic processes course in universities, the explanation of content related to the Poisson process tends to be abstract. This results in students having only a superficial understanding of this knowledge, making it difficult to effectively cultivate their ability to apply theories in practice. Taking the construction of a default model for residential mortgage loans as a specific case, this paper adopts a teaching method that integrates theory with application. It incorporates the definitions and properties of the Poisson process into modeling practice, thereby facilitating students’ progressive learning of the Poisson process. Throughout this process, students’ logical thinking ability is honed, and their capacity to apply the theoretical knowledge they have learned to solve practical problems is developed.