Hawkes processes in insurance: Risk model, application to empirical data and optimal investment
研究了基于复合霍克斯过程的索赔到达风险模型，证明其适合拟合保险数据，并推导了扩散近似以计算破产概率，进而分析该过程对保险公司最优投资策略的影响。
In this paper we study a risk model with claim arrivals based on general compound Hawkes processes and show that it is suitable to model empirical insurance data. We review a law of large numbers and functional central limit theorem for this model and derive a pure diffusion approximation which allows analytical calculation of finite-time and infinite-time ruin probabilities. We use the approximation to study the influence of replacing the classical Poisson arrival process by a general compound Hawkes process on optimal investment strategies for an insurer in an incomplete market by applying results from asset–liability management.