In this paper, we study some state-specific one-sided exit probabilities in a Markov-modulated risk process including the probability that ruin occurs without or with the surplus visiting certain states; the probability that ruin occurs without or with a claim occurring in certain states; the probability that the surplus attains a target level without or with visiting certain states; and the probability that the surplus attains a target level without or with a claim occurring in certain states. We also investigate the corresponding two-sided first exit probabilities without (or with) the surplus visiting certain states or without (or with) claims occurring in certain states. All these probabilities can be expressed elegantly in terms of some modified matrix scale functions which are easily computable.

中文翻译：

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马尔可夫调制风险模型中某些状态特定的退出概率

在本文中，我们研究了在马尔可夫调制的风险过程中一些特定于状态的单边退出概率，包括在没有或有盈余到达某些州的情况下发生破产的可能性；在某些状态下没有或有索赔要求发生破坏的可能性；在没有访问某些州的情况下，盈余达到目标水平的可能性；在某些州没有或有索赔发生的情况下，盈余达到目标水平的可能性。我们还研究了相应的双向第一出口概率，而没有（或有）盈余访问某些州，或者没有（或有）在某些州发生索赔。所有这些概率都可以用易于计算的一些修改后的矩阵比例函数优雅地表达。