论文标题
马尔可夫射击环境中的破坏概率
Ruin Probabilities in a Markovian Shot-Noise Environment
论文作者
论文摘要
我们考虑了一个具有计数过程的风险模型，其强度是马尔可夫射击过程，以解决Cramér-Lundberg模型的缺点之一，即Poisson过程的恒定跳跃强度。由于这种结构，我们可以将PDMP的理论应用于包含强度和储备过程的多元过程中，这使我们能够识别一个Martingales家族。最终，我们使用测量技术的更改来得出该模型中毁灭概率的上限。利用射击过程的复发结构，即使是毁灭概率的渐近行为也可以确定。
We consider a risk model with a counting process whose intensity is a Markovian shot-noise process, to resolve one of the disadvantages of the Cramér-Lundberg model, namely the constant jump intensity of the Poisson process. Due to this structure, we can apply the theory of PDMPs on a multivariate process containing the intensity and the reserve process, which allows us to identify a family of martingales. Eventually, we use change of measure techniques to derive an upper bound for the ruin probability in this model. Exploiting a recurrent structure of the shot-noise process, even the asymptotic behaviour of the ruin probability can be determined.
