标题： 基于广义复合霍克斯风险模型 显示英文标题

标题： Risk Model Based on General Compound Hawkes Process

摘要： 在本文中，我们引入了一个基于一般复合霍克斯过程（GCHP）的索赔到达风险过程的新模型。我们称之为基于一般复合霍克斯过程的风险模型（RMGCHP）。证明了大数定律（LLN）和泛函中心极限定理（FCLT）。我们还研究了这个新风险模型的主要性质，净盈利条件、保费原则和破产时间（包括最终破产时间），应用RMGCHP的LLN和FCLT。我们展示，作为我们结果的应用，基于复合霍克斯过程的风险模型（RMCHP）的类似结果，并将其应用于基于复合泊松过程的经典风险模型（RMCPP）。 显示英文摘要

摘要： In this paper, we introduce a new model for the risk process based on general compound Hawkes process (GCHP) for the arrival of claims. We call it risk model based on general compound Hawkes process (RMGCHP). The Law of Large Numbers (LLN) and the Functional Central Limit Theorem (FCLT) are proved. We also study the main properties of this new risk model, net profit condition, premium principle and ruin time (including ultimate ruin time) applying the LLN and FCLT for the RMGCHP. We show, as applications of our results, similar results for risk model based on compound Hawkes process (RMCHP) and apply them to the classical risk model based on compound Poisson process (RMCPP).