In this paper, a discrete Markov-modulated risk model with delayed claims, random premium income, and a constant dividend barrier is proposed. It is assumed that the random premium income and individual claims are affected by a Markov chain with finite state space. The model proposed is an extension of the discrete semi-Markov risk model with random premium income and delayed claims. Explicit expressions for the total expected discounted dividends until ruin are obtained by the method of generating function and the theory of difference equations. Finally, the effect of related parameters on the total expected discounted dividends are shown in several numerical examples.

中文翻译：

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具有随机保费收入和延迟索赔的离散Markov调制风险模型

本文提出了一种离散的马尔可夫调制风险模型，该模型具有延迟索赔，随机保费收入和恒定红利壁垒。假设随机保费收入和个人索赔受到状态空间有限的马尔可夫链的影响。提出的模型是具有随机保费收入和延迟索赔的离散半马尔可夫风险模型的扩展。通过生成函数的方法和差分方程的理论，获得了直到破产为止的总预期折现红利的显式表达式。最后，几个数值示例显示了相关参数对总预期折现股利的影响。