A Risk Model with an Observer in a Markov Environment
A Risk Model with an Observer in a Markov Environment
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DOI：
10.3390/risks1030148
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发表时间：
2013-10
影响因子：
1.9
通讯作者：
Hansjoerg Albrecher;J. Ivanovs
中科院分区：
文献类型：
--
作者：
Hansjoerg Albrecher;J. Ivanovs
我们考虑谱负马尔可夫可加过程作为随机环境中风险过程的模型。继最近的兴趣替代破产的概念，我们假设破产发生时，一个独立的泊松观察员认为该过程是消极的，其中的观察率可能取决于环境的状态。使用近似参数和谱理论，我们建立了一个明确的公式，由此产生的生存概率在这个一般设置。我们还讨论了一个有效的评估所涉及的数量，并提供了一个数值例子。
We consider a spectrally-negative Markov additive process as a model of a risk process in a random environment. Following recent interest in alternative ruin concepts, we assume that ruin occurs when an independent Poissonian observer sees the process as negative, where the observation rate may depend on the state of the environment. Using an approximation argument and spectral theory, we establish an explicit formula for the resulting survival probabilities in this general setting. We also discuss an efficient evaluation of the involved quantities and provide a numerical illustration.