Joint distributions of some actuarial random vectors for the Cox risk model

作者：Xu Lin; Wang Rongming^*; Yao Dingjun

来源：Applied Stochastic Models in Business and Industry, 2012, 28(5): 420-429.

DOI：10.1002/asmb.916

• Actuarialrandom vector
• Cox risk model
• ruin time
• operational time scale

The main purpose of this paper was to investigate the joint distributions of some actuarial vectors that contain the ruin time for the Cox risk model. Joint distributions of some actuarial vectors such as those containing the ruin time, the maximum surplus before ruin, duration of the surplus being negative, and others are important for measuring the risk management level and the severity caused by ruin. In the past decade, great literatures have devoted to the study of these distributions for classical models, such as the compound Poisson model and the perturbed compound Poisson model etc. The main result of this paper provides the joint distributions of these actuarial vectors for the Cox risk modela model with wide applications in risk theory. The main method of this paper is to apply the idea of operational time scale to the Cox model, which enables us to solve our problem by intergrading some existing results for the compound Poisson risk model. To some extent, we can view our work as an extension of joint distributions of some actuarial vectors for the compound Poisson risk model to the ones for the Cox risk model.

• 出版日期2012-10
• 单位华东师范大学; 南京财经大学; 安徽师范大学