论文标题
复合多元霍克斯过程：较大的偏差和罕见的事件模拟
Compound Multivariate Hawkes Processes: Large Deviations and Rare Event Simulation
论文作者
论文摘要
在本文中，我们为由带随机标记的多元霍克斯工艺引起的多元化合物过程建立了一个较大的偏差原理。我们的证明取决于显示多元化合物过程的限制累积液的基本平滑度，从而解决了固有的并发症，即该累积物是通过固定点表示隐式表征的。我们采用大型偏差原理来得出相关多元风险过程的边际破坏概率的对数渐近结果。我们还展示了如何使用重要性抽样在此多元设置中进行罕见的事件模拟，并证明了基于重要性采样器的渐近效率。该论文以对我们罕见事件模拟程序的性能进行系统评估结论。
In this paper, we establish a large deviations principle for a multivariate compound process induced by a multivariate Hawkes process with random marks. Our proof hinges on showing essential smoothness of the limiting cumulant of the multivariate compound process, resolving the inherent complication that this cumulant is implicitly characterized through a fixed-point representation. We employ the large deviations principle to derive logarithmic asymptotic results on the marginal ruin probabilities of the associated multivariate risk process. We also show how to conduct rare event simulation in this multivariate setting using importance sampling and prove the asymptotic efficiency of our importance sampling based estimator. The paper is concluded with a systematic assessment of the performance of our rare event simulation procedure.
