马氏调节风险模型下的破产前盈余分布

On the Distribution of the Surplus Before Ruin in a Markov-Modulated Risk Model

对在马氏调节风险过程中破产前盈余和破产时赤字的联合分布进行研究.该过程中的泊松索赔到达速率和索赔额分布随时间改变,并取决于1个潜在的马尔科夫跳过程的状态.推广了Dickson公式,并证明了破产前盈余的分布函数和密度函数均能由破产概率表示出来.

The joint distribution of the surplus before ruin and the deficit at ruin in a Markov-modulated risk process in which the rate for the Poisson claim arrivals and the distribution of the claim sizes vary in time depending on the state of an underlying （external） Markov jump process is studied.The Dickson′s formula from the classical risk model to the Markov-modulated risk model is extended and it is shown that both of the distribution function and density function of the surplus before ruin can be expressed in terms of the ruin probabilities.