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Joint distributions of some actuarial random vectors for the Cox risk model
Author(s) -
Lin Xu,
Rongming Wang,
Dingjun Yao
Publication year - 2011
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.916
Subject(s) - poisson distribution , joint probability distribution , risk model , ruin theory , proportional hazards model , joint (building) , econometrics , mathematics , extension (predicate logic) , statistics , computer science , actuarial science , economics , engineering , architectural engineering , programming language
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 model—a 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. Copyright © 2011 John Wiley & Sons, Ltd.