期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
Adjoint Multi-dimensional Markov Processes of a q-risk Model
摘要/Abstract
q-风险模型是Q-风险模型的推广，而Q-风险模型又是经典风险模型的推广.在Q-风险模型中，索赔时刻是一个规则Q-过程的跳跃时刻，而索赔计数过程是马尔可夫到达过程（MAP）的计数过程，Q-风险模型被一个环境过程控制.环境过程是一个规则Q-过程，它取离散的实数值.实际问题中，环境过程可以取连续的实数值.因此，需要将环境过程Q-过程推广为q-过程，并进一步将Q-风险模型推广为q-风险模型.证明了q-风险模型的伴随2-维和3-维随机过程都是时齐马尔可夫过程，并求出了它们的初始分布和转移概率的显式表示式.作为q-风险模型的特殊情形，对Q-风险模型获得了相应的结论.
A q-risk model is a generalization of a Q-risk model,and a Q-risk model is a generalization of the classical risk model. In a Q-risk model the moments of claims are exactly the jumping moments of a regular Q-process and the counting process of claims is the counting process of a Markov arrival process (MAP).The Q-risk model is controlled by an environment process.The environment process is a regular Q-process taking discrete real values.In practice an environment process may take general real values.So the environment process Q-process needs to be extend to a q-process.Furthermore a Q-risk model needs to be extend to a q-risk model.It is proved that the adjoint 2-dimensional and the 3-dimensional processes of a q-risk model are time-homogeneous Markov processes.The analytic expressions of their initial distributions and their transition probabilities are calculated.As a special case of a q-risk model the corresponding some results of a Q- risk model are obtained.
关键词
参考文献 13
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