Lévy过程的偏度溢价

具有水平依赖保费率的风险过程的概率方法

Probabilistic approach to risk processes with level-dependent premium rate

针对水平依赖保费率的风险过程，提出一种纯概率方法，通过分析渐近零漂移Markov链，得到保费率收敛至净利润临界值时破产概率的上下界，区别于现有文献结果。

具有随机保费的风险过程的有限区间出口

On the exit from a finite interval for the risk processes with stochastic premiums

本文考虑了几乎半连续的分步过程$ξ(t)$。$ξ(t)$跳跃的条件特征函数具有$\mathrm{E} [ e^{iαξ_k}/ξ_k>0 ]=c(c-iα)^{-1}$的形式。对于这样的过程的边界泛函与有限区间的出口进行了研究。

保费与索赔到达率随机相关的破产问题

Ruin under stochastic dependence between premium and claim arrivals

我们调查，专注于破产概率，适应的Cramer-Lundberg模型的盈余过程的保险公司，在其中，有条件的强度，两个混合泊松过程的到达时间的保费和索赔分别，是独立的。这样的模型表现出的总保费和索赔额的过程之间的随机依赖性。当索赔额和保费均服从指数分布时，得到了破产概率的显式表达式。

An expansion formula for Hawkes processes and application to cyber-insurance derivatives

In this paper we provide an expansion formula for Hawkes processes which involves the addition of jumps at deterministic times to the Hawkes process in the spirit of the well-known integration by parts formula (or more precisely the Mecke formula) for Poisson functional. Our approach allows us to provide an expansion of the premium of a class of cyber insurance derivatives (such as reinsurance contracts including generalized Stop-Loss contracts) or risk management instruments (like Expected Shortfall) in terms of so-called shifted Hawkes processes. From the actuarial point of view, these proce…

Brownian Motions on Metric Graphs with Non-Local Boundary Conditions I: Characterization

A classification for Brownian motions on metric graphs, that is, right continuous strong Markov processes which behave like a one-dimensional Brownian motion on the edges and feature effects like Walsh skewness, stickiness and jumps at the vertices, is obtained. The Feller property of these processes is proved, and the boundary conditions of their generators are identified as non-local Feller-Wentzell boundary conditions. By using a technique of successive revivals, a complete description of the generator is achieved for Brownian motions on star graphs.